ON THE DYNAMICS OF DRAW TEXTURING
by
David Stuart Brookstein
B.T.E., Georgia Institute of Technology
(1971)
S.M., Massachusetts Institute of Technology
(1973)
SUBMITTED IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF SCIENCE IN
MECHANICAL ENGINEERING
AT THE
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
February, 1976
Signature of Author
Department of Mechanical Engineering, August 28, 1975
by..... .
Certified
Accepted by
....
.......
esis Supervisor
...............................
Graduate
Chairman, Department Committee Gctn
Students
'
ARCv
c-t
A
$
976
ON THE DYNAMICS OF DRAW TEXTURING
by
DAVID STUART BROOKSTEIN
Submitted to the Department of Mechanical Engineering on
August 11, 1975 in partial fulfillment of the requirements
for the Degree of Doctor of Science.
ABSTRACT
This study is concerned with the mechanics and dynamics
of a process for increasing bulk, softness, cover and stretch
of thermoplastic continuous filament yarns. In particular
this investigation focuses on the interactions between the
feed yarn and the texturing machine in the draw texturing
process. It treats the cases of both steady state and
transient operation. The degree of filament drawing, the
cold, hot, cooling and post spindle twist distributions,
the threadline tension, and the threadline torque are shown
to possess a non-linear relationship dictated by machinematerial parameters. This study presents a tractable model
for determining analytically threadline torque, tension,
and twist distributions,- given information on machine
settings and on material properties. Considerable
attention is devoted to the determination of twist distribution in the threadline during transient operation.
The results of numerous observations of threadline response
were compared with the data generated from the analysis of
threadline operation. In general, the agreement between
theory and experiment is good.
Thesis Supervisor:
Title:
Stanley Backer
Professor of Mechanical Engineering
ACKNOWLEDGMENTS
I would like to thank E.I. du Pont de Nemours and
Company, Burlington Industries, and Westvaco for their
financial support during my stay at M.I.T.
Extra thanks
go to Du Pont for supplying the yarns used for this study.
I am gratefully indebted to Professor J.J. Thwaites of
the University of Cambridge for his fruitful suggestions
and critical appraisal of this work during his stays at
the Fibers and Polymers Laboratories at M.I.T.
I would also like to convey my appreciation to Dr.
Subhash K. Batra, Mr. Steven C. Smith, and Dr. Raymond Z.
Naar for their helpful conversations with regard to this
study.
Without Ms.
Guddi Wassermann-Ladda the completion of
this work might have taken a longer time to materialize
than it did.
Her superior laboratory skills were used to
the fullest advantage in accumulating the data needed for
this study.
To her goes my sincerest gratitude.
I would like to thank Ms. Laurel Silverman for performing
the Herculean task of typing this manuscript.
Over the years my stay at M.I.T. was made that much
more pleasant by my acquaintance with Miss Dorothy Eastman.
Her assurance helped me through many trying days.
Finally, I would like to thank my supervisor Professor
Stanley Backer.
However, I am unable to adequately express
my appreciation in words for his guidance, appraisal, and
above all his patience. His support of my work over the
last four years will always be remembered.
fitting expression I have is thank you.
The only
to Sue and Kara
TABLE OF CONTENTS
ON THE DYNAMICS OF DRAW TEXTURING
Page
9
1.
Introduction
2.
Steady State Operation
18
2.1
Introduction
18
2.2
Method of Solution
20
2.3
Steady State Threadline Mechanics
2.3.1 Continuous Twisting of Filament Yarns
30
2.3.2
Cold Zone Twist Contraction
31
2.3.3
Flow Continuity in Cold Zone
35
2.3.4
Cold Zone Tension
37
2.3.5
Cold Zone Torque
37
2.3.6
Hot Zone Tension
39
2.3.7
Hot Zone Torque
43
2.3.8
Calculation of Twist
44
2.3.9
Calculation of Hot Twisted Yarn
46
Velocity
2.3.10 Calculation of Yarn Radii
2.3.11
2.4
Experimental Study of Steady State Draw
2.4.1
2.4.2
3.
49
52
Summary
54
Texturing
2.5
30
Materials and Texturing Apparatus
Results and Discussion
54
56
Effect of Materials Properties on Steady State
Threadline Behavior
64
Transient
68
Operation
3.1
Introduction
68
3.2
Observations of Torsional Behavior of the
70
Texturing Threadline
6
Page
3.2.1
Experiments Using Pre-Drawn PET Yarns
3.2.2
Experiments Concerning Transient Twist,
Using Pre-Drawn PET Yarns
3.2.3
Experiments Using POY PET Yarn
3.2.4
Experiments Concerning Transient Twist,
Using POY PET Yarns
3.3
70
91
104
109
Analysis of Transient Operation
116
3.3.1
Introduction
116
3.3.2
Method of Solution
117
3.3.2.1
Model 1: Flat Twist Distribution
126
3.3.2.2
Model 2: Tilted Twist Distribution
128
3.3.3 Transient Threadline Mechanics
3.3.3.1 General Tension and Torque
Relationships
3.3.3.2
132
132
General Material and Turn Balances
for the Hot Zone and the Post Spindle
Zone
3.3.3.3
144
Material and Turn Balances for the
Cold and Cooling Zones: Model 1 Flat Twist Distribution
3.3.3.4
148
Twist Transport Material Balances
and Turn Balances in the Cold and
Cooling Zones: Model 2 - Tilted
Twist Distribution
3.3.4
Solution Technique for the Transient
171
Analysis
3.4
158
Experimental Study of Transient Operation of
the Draw Texturing Process:Using POY Polyester
173
3.5
Experiments on the Draw Texturing of POY Nylon
193
3.6
Predicted Effect of Oscillatory Operation on
Threadline Response
3.6.1 Oscillating Spindle Speed
201
201
7
Page
3.7
3.6.2
Oscillating Feed Roller Surface Speed
3.6.3
Oscillating Take Up Roller Surface
202
Speed
Effect of Increasing Yarn Wrap Angle on
204
Spindle
205
4.
Periodic Twist Slippage
210
5.
Conclusions and Summary
225
6.
Suggestions for Continuing Research
232
Bibliography
235
Appendix 1: Interia Effects on Threadline
238
Appendix 2: Experimental Values of Threadline
Tension and Torque
Appendix 3: Hot Draw Curves POY PET
239
Appendix 4: MITEX Torque - Tension Meter
Appendix 5: Computer Program for Steady State
244
Analysis
243
247
Appendix 6: Computer Program for Transient Analysis
8
253
Chapter
1
INTRODUCTION
Texturing is a process whereby yarn stretch, bulk, absorbency, and improved hand are provided through the introduction
of "permanent" crimp into otherwise straight continuous filaments.
Fabrics made from textured yarns have captured a
large share of the textile apparel market.
The popularity
of garments made from textured yarns results from improved
wear performance, freedom from wrinkling, and high bulk or
cover power.
Yarn texturing can be accomplished by any one of at least
a dozen techniques; however, most texturing is accomplished
by the false twist process.
This single process sequentially
twists, heat sets, and untwists a thermoplastic filament
bundle in a continuous operation.
A schematic diagram show-
ing the yarn path through a typical pin-spindle false twist
machine is pictured in Figure 1.1.
Yarn is removed from the supply package, fed at a controlled rate over the heater, through the false twist pinspindle, and then onto a takeup package.
Twisted yarn mov-
ing between the feed rollers and spindle is heat set before
passing through the rotating spindle.
The elements of false twisting can be presented rather
simply.
If a stationary multifilament yarn is held at both
9
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H
H
rz-
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ends and twisted by a spindle at its center, equal amounts of
twist with opposite directions of spirality will be imparted
to each side, as seen in Figure
1.2.
If each half of the yarn is cont
ZZZ
.
sidered separately, it is observed
that the twist is real; however,
the algebraic sum of twist through-
Figure 1.2
out the yarn is zero.
Now with the
twisting element rotating continuously and yarn moving through it,
the twist on the downstream side
...zz. { #'
Z',
of the spindle is carried away
through the take-up rollers and
Figure 1.3
twist from the upstream side of
the twister moves across the spindle to the downstream side.
Once
a yarn segment has moved through the twisting element, the
twisting direction relative to that yarn segment is reversed
and the segment is untwisted.
At the same time, more twist
is inserted at the feed rollers so that at steady state operation, a stationary zone of twisted yarn appears upstream
of the spindle and twist free yarn occupies the downstream
zone.
This condition is illustrated in Figure 1.3.
Twisting can be performed either by a pin-spindle or by a
friction bushing.
The yarn paths on each such spindle are
11
shown in Figure 1.4.
For the pin-spindle system operating
at steady state the segment of yarn which is about to enter
the spindle generally rotates once for each spindle rotation.
In the bush system the yarn will rotate %ushing/Ryarn
times
for each bush rotation, provided that no rotational slippage
occurs.
However, in virtually all friction twisting, rotat-
ional slippage does occur at the spindle.
The ratio of bush-
ing to yarn rotation varies from machine to machine and from
This thesis deals with the
time to time on a given machine.
pin-spindle twisting system which dominates in the U.S. textile industry at present.
In the pin-spindle system, a heater is placed in the upstream zone, between the feed rollers and the spindle, with
enough space left for the yarn to cool before being untwisted
at the spindle.
This upstream zone is termed the texturing
zone, in which continuous twisting, heat setting and cooling
are carried out, followed by untwisting downstream of the
spindle.
The presence of the heater causes two levels of
twist to occur in the threadline in the texturing zone for
reasons to be discussed later.
However, threadline tension
and torque along the texturing zone are uniform.
A schematic
diagram of the threadline characteristics during steady state
operation is shown in Figure 1.5.
Until recently, most feed yarns for texturing were manufactured by fiber producers, via extrusion and drawing.
12
Figure 1.4
.--- YARN
V
FRICTION BUSHING
PIN-SPINDLE
13
Figure 1.5
I
I
I
I
I
'4
I
TEXTURING ZONE
Typica
I
Thread li ne
14
J
Characteristics
Texturing of this fully drawn yarn was then undertaken by the
textile manufacturer.
In 1966 Mey (
) reported on studies
of the combination of drawing and texturing processes.
By
1972 selected American and European fiber producers began to
integrate drawing processes with false twist texturing.
This
innovation is called false twist draw-texturing or simply,
draw texturing.
There are two basically different methods of draw texturing: the sequential process and the simultaneous process.
In the sequential process, the drawing operation, which preceeds false twisting, is carried out in a separate zone on
the machine.
Since the local processes of drawing and tex-
turing are thus isolated in the sequential process, the
resulting yarns are essentially the same as those produced
from previously drawn yarn by the conventional texturing
process.
In the simultaneous process, the yarn moves into
the cold portion of the texturing zone where it receives some
cold twist.
At or near the entrance to the heater further
twisting occurs and at this point the yarn draws, both
actions taking place simultaneously.
Yarns produced in this way show several distinct differences from conventional false twist textured yarns and from
those draw textured yarns produced by the sequential process,
the most important difference being that fabrics made from
simultaneously draw textured yarns have a more uniform dyed
15
appearance than those made from conventional false twist textured yarns. ( 2)
Thwaites shows that this superiority is
associated with the modified light reflectance of the simultaneously drawn yarns
(2)
This thesis will deal primarily with that simultaneous
draw texturing process which employs pin-spindle twisting.
One problem encountered with the simultaneous draw texturing process is that when essentially unoriented amorphous
polyester is used as the feed yarn, the filament bundle loses
strength and/or the separate filaments fuse together as soon
as the yarn is heated above its glass transition temperature
for several seconds (3)
As a result, "stringup" of the
texturing machine becomes very difficult.
A solution to this
problem is to use a relatively amorphous, yet somewhat preoriented, polyester feed yarn, which does not soften and
lose its strength as rapidly upon heating.
This preoriented
polyester yarn (POY PET) can be produced simply by high speed
winding of the freshly extruded filament bundle, without the
provision of a separate drawing operation.
Thus, there is a
major economic advantage in the production of partially oriented yarn (rather than conventionally drawn yarn) and in its
usage as feed stock for simultaneous draw texturing processes.
For the latter methods employ yarns which have been ex-
truded and partially drawn in a single process while conventional texturing requires yarns which are drawn to their final
16
draw ratio in a process separate from the extrusion process.
A successful draw texturing operation depends on the quality of its feed yarn as well as on the control of its process
to produce consistently uniform quality yarn on an hour to
hour and day to day basis.
Once a draw-texturing machine is
adjusted for a given operation, the textile manufacturer expects it to produce large quantities of yarn possessing uniform crimp with no residual twist.
In mechanical terms this
implies threadline torque and tensions which are constant in
time from spindle position to position in a given machine and
from machine to machine.
Any variation experienced in gen-
eralized threadline forces (tension or torque) may cause
variation in crimp level or in subsequent dyeing behavior
of the output yarn or it may introduce real twist in the post
spindle region as a consequence of periodic twist slippage
past the rotating spindle.
The textured yarn producer must
make certain decisions as to the setting of machine and/or
material parameters, on the basis of resulting product quality.
As of this time, such decisions are made on the basis
of preliminary experimental trials or in accordance with past
production experience.
This thesis seeks to provide a quan-
titative basis for anticipating the effect of variations in
feed material properties and of machine parameters on the
draw texturing process during both steady and non-steady
operation.
17
Chapter
2
STEADY STATE OPERATION
2.1
INTRODUCTION
False twist draw texturing is a textile process which
manifests strong interactions between feed material and machine.
Once the texturing machine is set for given feed and
take-up roller velocities, spindle speed, and texturing zone
heater temperature, the yarn being processed reacts to the
given machine conditions by twisting, drawing, uptwisting,
heat setting and untwisting.
The degree of filament drawing,
the cold, hot and cooling twist levels, the threadline tension, and the threadline torque are determined by a complex
non-linear relationship of machine-material parameters.
block diagram of the process is shown in Figure 2.1.
A
A full
understanding of this diagram must await the detailed analysis of texturing mechanics to be presented later, but it
suffices at present to emphasize certain essential features
of its construction.
Note first that all mass flow moves
from left to right, i.e. from feed roller to take up roller.
Second, the twist originates at the spindle and moves to its
left, upstream, or to its right, downstream.
Finally, gen-
eralized threadline forces operating at each station of the
texturing zone interact directly.
This section provides a tractable model for analytically
18
z
p:
H
x
H
E-1
H
U)
H
Ed
H
U)
0
H
U
H
H
U
C)
q
U)
z
H
P
U)
E[
U
H
a.
U)
H
E
E-1
H
H
H
U)
H
H
U
O
Z
H
E-
e
19
>I
H
H
8
W
rZ4
r--
0)
determining threadline torque, tension, and twist distribution, given information on machine settings and on material
Later, these analytical solutions will be com-
properties.
pared with experimental data to test the validity of the
model.
In addition, a parametric survey will be presented
to show the effect of different feed yarn properties on
threadline behavior.
2.2
METHOD OF SOLUTION
The false twist draw texturing process can be divided
into zones as shown in Figure 2.2.
Figure
2.2
SPINDLE
V4
Vo
U
COLD
HEATER
COOLING
ZONE
ZONE
V
V
V
V
0
2
3
4
POST
SPINDLE
ZONE
= Feed roller linear velocity
= Linear velocity of cold twisted yarn
= Linear velocity of hot twisted yarn
= Take up roller linear velocity
W s = Angular velocity of false twist spindle
In this device, yarn enters the cold zone, twists, tra-
20
verses to the heater, simultaneously draws and uptwists,
cools, progresses to the spindle, crosses the spindle and untwists.
Between the feed rollers and the spindle, threadline
torque and tension are considered uniform since for our particular system, negligible friction occurs between the yarn
and the heater plate.
Because of the extremely small yarn
masses involved inertial effects are considered negligible
for the rotating threadline.
Justification of this assump-
tion is given in the Appendix 1.
Since the threadline torque
and tension are uniform along the texturing zone, we can
chose any yarn cross section in this zone for the purpose of
analyzing tension and torque.
For this analysis we must
determine the local material-system constitutive relations,
the local yarn geometry, and the system compatibility at
each cross section.
As a first approach, the pin-spindle texturing machine can
be thought of as a device that deforms yarn at both cold and
hot temperatures.
The feed rollers, the take up rollers, and
the rotating false twist spindle are the deforming devices;
the heater is the temperature treatment device.
Generalized
threadline forces, i.e. torque and tension, are consequences
of the deformation and temperature treatment.
During steady
state operation, the condition of 100% pin-spindle efficiency
is defined as the condition when the cooling yarn segment
about to enter the spindle, rotates once for every turn of
21
that spindle.
It is assumed that the hot yarn segment up-
stream of the cooling zone rotates at this same velocity
since experimental observations of twist distribution in the
threadline show relatively little difference between hot and
cooling zone twist levels (4
The system can also be
thought of as running at steady state if there is continual
rotational slippage of the cooling yarn relative to the spindle.
For example, in the case of 80% efficiency, the cooling
yarn segment will rotate 0.8 times for every turn of the
spindle.
This analysis will consider the case for 100%
efficiency; however, if the efficiency were given, that case
could be easily handled with the present analysis.
During steady state operation, the yarn in the cooling
zone progresses downstream one twist pitch for each spindle
rotation.
As this yarn moves through the spindle, the spin-
dle untwists one turn of twist and the given pitch length is
untwisted completely.
In the case of non-steady operation
this condition of one twist pitch of linear motion per spindle revolution need not prevail.
Treatment of the non-
steady state condition follows in Chapter 3.
As the untwisted filaments enter the cold zone, they are
strained and twisted, the net result being that the filament bundle contracts longitudinally.
This contraction
results in a reduction of yarn linear velocity according to
continuity requirements.
The mechanics of cold zone twist
22
contraction is examined in Section 2.3.2.
The physical motivation for the yarn to twist upon entry
into the cold zone is the existence of a threadline torque
field.
In Section 2.3.4 we show that cold zone tension is a
function of cold zone twist and cold filament strain.
We
can express cold zone yarn tension as a function of certain
unknowns of the system:
Tcold
where
zone
(2-1)
1 (ecold'c)
ecold = cold filament strain
P c = cold zone twist (radians/unit twisted length)
Cold zone yarn torque has one component due to filament
tension and one due to filament bending
ing.
and filament twist-
Since the filaments in the twisted yarn are constrained
to lie approximately in right cylindrical helices, they are
bent and twisted about their individual axes.
The filament
bending and torsional moments resulting form this deformation
can be resolved along the yarn axis so as to determine their
contribution to total threadline torque.
Platt el al. ( 5 )
has analytically determined this relation, showing that yarn
torque due to fiber torsion and bending is a function of the
torsional rigidity of the fiber, its bending rigidity, and
its geometrical path in the yarn structure.
Accordingly,
we can express cold zone yarn torque due to fiber bending
and torsion as
23
Mt cold zone (bending, torsion) =F2
(EI, GIP
)
(2-2)
where
EI = fiber bending rigidity
GI
P
c
P
= fiber torsional rigidity
= cold zone twist
Filament tension can be readily determined from filament
strain and can then be radially resolved and multiplied by
the appropriate radius (corresponding to the filament position in the yarn structure) to determine the individual tensile component of yarn torque.
be expressed
This tensile component can
as:
Mt cold zone (tension) = F3
(ecold'
P)
(2-3)
Combining (2-2) and (2-3) we can express the total torque in
a yarn section from the cold zone as
Mtc= F (Pc, ecold'EIGIp)
EI and GI
p
(2-4)
are known properties of the filaments.
ecold are unknown and must be determined.
Pc and
c
Therefore there
are two equations with four unknowns relating to the threadline in the cold zone, i.e.:
Mtc; Tc; ec; Pc
In order to generate more independent simultaneous equations it is necessary to choose another threadline cross section with different geometry, different material-system con-
24
stitutive relations, and different system compatibility.
Towards this end, a cross section of the hot drawn yarn at
the base of the threadline drawing "neck" is analyzed.
In
section 2.3.6 we demonstrate that hot zone filament tension
is a function of both hot and cold zone yarn twist, cold and
hot yarn linear velocity, and the hot draw material-system
constitutive relation.
On the assumption that the material
constitutive relation, MCR, for the hot drawing yarn can be
determined, hot yarn tension can be expressed as:
hot zone
where
V
F5(V2 ,V3 ,P ,Ph,MCR)
(2-5)
= linear velocity of the cold yarn
2
V
= linear velocity of the hot yarn
3
Pc = cold zone twist (radians/unit twisted length)
h
hot zone twist (radians/unit twisted length)
Taking the component of filament hot tension perpendicular
to the yarn axis we can determine the contribution of tension to yarn torque in the hot zone:
M
t
(tension)
F (VV
6
2
3
P ~P(2-6)
P
c' h
This derivation is presented in Section 2.3.7.
The objective of the false twist texturing process is to
temporarily deform thermoplastic filaments into a twisted
configuration and then to stress relax them before untwisting by passing the twisted yarn over a heater whose temper-
25
ature is above the crystal melting temperature of the feed
yarn.
If this process is to be effective,
components
of yarn
torque due to fiber bending and fiber torsion should be relaxed out over the heater.
Naar
(6)
If this relaxation occurs, as
points out, the torque in the yarn over the heater
should be due primarily to individual fiber tension.
This
assumption is to some extent justified when one looks at the
twist distribution of the yarn over the heater.
Once the
torque due to cold fiber torsion and cold fiber bending is
relaxed, one observes a dramatic twist crankup at the heater
entrance which is necessary to keep the torque constant.
Total torque in the hot zone is primarily the torque due to
fiber tension and accordingly can be expressed as:
M
Mt hot zone
By equating
(2-1) and
M
Mt hot zone (tension)
(2-5) and equations
(2-4) and
(2-7)
(2-7)
(2-7),
which corresponds to equalizing tension and torque through
the threadline, we can reduce our system of equations to two
equations with five unknowns.
EI and GIp are assumed given.
These are shown for
Equal Tension in Cold and Hot Zones
= F(e
cold'Pc)
1
cold'c
- F5(V
5
26
2
,V 3 ,Pch Ph)
(2-8)
Equal Torque in Cold and Hot Zones
0
F(eoldPc
=
EI,GIp) - F(V
,V
,PcPh)
(2-9)
In Section 2.3.3 we show how cold filament strain is analytically related to cold yarn contraction and to the ratio of
feed roller velocity and translational velocity of the cold
twisted yarn.
Cold strain can be expressed as:
ecold = F(V,VoP
8
where
V
2
0
(2-10)
c
= Linear velocity in the cold zone
V
= Linear velocity of the feed roller
0
Pc = Cold twist (radians/twisted length)
As indicated, for steady state operation, the hot twisted
yarn segment progresses downstream one pitch length during
the time it takes for the spindle to rotate one revolution.
Therefore the linear velocity of the twisted cooling yarn
segment,
Vb, as it enters
Vb
1
2rP
where
s
the spindle is :
=
s
s
27Tw
5
P
(2-11)
5
Spindle speed, (radians per second)
It has been observed that the difference between local
twist in the cooling (therefore setting) zone, Ps, and the
local twist at the exit of the heater, Ph is negligible.
Likewise the difference between the linear velocity of the
27
threadline as it leaves the heater and as it enters the
spindle is considered to be negligible.
This permits a re-
writing of equation (2-11) in the form
Ph=
us/v
(2-12)
The spindle speed is a given quantity, therefore we need to
determine the threadline velocity at the heater exit V .
It
3
is shown in Section 2.3.9 that the given value of take up
roll velocity can be used to determine V
3
With the appropriate mathematical substitutions the system
of equations outlined in this section can be reduced to three
nonlinear simultaneous equations with three unknowns:
where
= u(V ,ec ,Pc) - V(V ,Pc)
(2-13)
0 = x(V ,e ,Pc) - Y(V ,Pc)
(2-14)
0 = z(V ,e ,Pc)
(2-15)
ec is ecold
Equations (2-13), (2-14), and (2-15) are solved by the com-.
puter subroutine "YARN " which is listed in Appendix 5
The
three equations are reduced to a single equation with the
unknown, Pc, and the value of Pc satisfying the single
equation is determined.
Given the value of Pc for a given
set of machine parameters, the corresponding values of V
and ec are then determined.
When the solution for Pc,ec, and
28
V
2
is found, they are substituted back into equations (2-1),
(2-5), (2-4) and
(2-7) to determine
the threadline
tension
and threadline torque.
In summary, this method of solution makes possible the
determination of the threadline tension, threadline torque,
and threadline twist distribution given the feed roller and
take up roller velocities, spindle speed, and the material
properties of the feed yarn.
It remains to provide specific
relationships for cold and hot tension, cold and hot torque,
hot twist, hot twist contraction, and cold twist contraction.
This is done in Section 2.3.
29
2.3
STEADY STATE THREADLINE MECHANICS
2.3.1
Continuous Twisting of Filament Yarns
As untwisted feed yarn is delivered by the feed rollers
into the texturing zone and is exposed to the threadline
torque, the yarn uptwists until its torque reaches that of
threadline.
As the yarn uptwists, its filaments are extended,
partially because of the threadline tension and partially
because of the tortuous path lengths the filaments are forced
to follow in conforming to the geometry of twists.
Filaments
lying on relatively high helix angles in the outer radial
layers of the yarn, are prone to extend to a greater extent
then filaments located closer to the yarn center.
The pres-
ence of such differential strain was first recognized by
Morton (
7)
who suggested that the magnitude of the different-
ial strains would be reduced with the occurrence of interchange between outer and inner filaments.
A continuing
interchange of this nature tends to equalize filament tensions throughout the yarn during steady state twisting.
This
cyclical interchange of fiber position is known as radial
migration.
Backer & Yang ( 4) demonstrated that radial mi-
gration does occur at the entrance to the texturing zone at
the feed rollers.
Naar(
)
On the basis of these observations
assumed that the filaments in the cold yarn segment
of the texturing zone are under equal tension.
this assumption as part of our model system.
30
We adopt
2.3.2
Cold Zone Twist Contraction
When yarn is twisted under a given tension it will contract because of the longer path lengths that the outer filaments must follow.
The resulting contraction is quantitized
by a "contraction factor" defined as:
Cr
Length of Zero Twist Yarn
Length of Twisted yarn
-
(2-16)
The length of a projected segment
of a filament
lying in a twisted
5Lsec
set0
4
yarn is compared with the same
length of filament in an untwisted
"'.
i
%.%
yarn in Figure 2.3.
The con-
I
--- J
traction factor of the filament
yarn segment of Figure 2.3 is obviously sec
.
Figure 2.3
31
Hearle's Model of Twist Contraction
Consider a twisted yarn of length h as shown in Figure 2.4.
Figure 2.4
Illi1llt'
Th
l1111111
1
1
=
lllll
II
lit'
h sec e
I
Hearle ( 8) assumes that because of radial migration the
difference in the path length of twisted filaments in a given
segment of yarn vs. the length of the twisted yarn is spread
uniformly over all the filaments in a relatively long segment of yarn.
He shows that the distribution of lengths in
a short segment is linear and therefore the contraction
factor equals the arithmetic average of the minimum filament
length (equal to yarn length) and maximum filament length
(for outside layer).
The contraction factor for this yarn
model is
32
C
r
- (l+sec)
2
(2-17)
where 8 is the surface helix angle of the yarn.
Alternative Model of Twist Contraction
Hearle's model of twist contraction essentially averages
the length of the filaments in a yarn segment over its cross
Alternatively we can average the filament
sectional area.
lengths over the yarn radius.
This method will disproportion-
ately weigh the average towards a lower value than that obtained from Hearle's model since there are fewer fibers in
central yarn radial positions compared to the number of fibers in outer radial positions.
The alternative model for
twist contraction is formulated as
R
Cr
-
sec dR
~RdR
(2-18)
Cr = 1/2[ ln(tanS+secO) + sec]
or
The predicted value of contraction factor using either
model must be compared with the measured values.
Experimen-
tal values of twist contraction in the cold zone are compared to the predicted values using both models below for five
different cold segments derived using different machine
twists.
33
COLD YARN TWIST CONTRACTION
Machine Twist
Measured*
Hearles' Model
Alternative Model
50
1.053
1.091
1.063
60
1.139
1.190
1.136
65
1.158
1.207
1.148
70
1.165
1.213
1.153
80
1.191
1.247
1.178
Comparison of the measured values to both models indicates
that the alternative model for twist contraction in the cold
zone predicts closer values to the measured ones.
Nonethe-
less, both models will be included separately in the steady
state prediction of threadline behavior (i.e., threadline
tension, threadline torque, cold threadline twist, and hot
threadline twist.)
*By untwisting in a twist testerlyarn segments which had been
twisted in the texturing apparatus.
ing equalled the texturing tension.
34
The tension of untwist-
Flow Continuity in Cold Zone
2.3.3
During steady state operation of the texturing process,
the product of the linear density of the yarn and the local
translational yarn velocity (mass flow rate) must be constant
at any station in the texturing threadline, i.e.
(2-19)
D VIX = constant
where
D = Yarn denier (linear density)
V = Linear velocity of yarn
X = Linear location on threadline, i.e. its station
The linear density of a textile yarn is usually expressed in
terms of its denier, defined as the weight in grams of 9000
yarn meters.
The machine configuration between the feed rollers and the
cold zone is illustrated
in Figure
2.5
Figure 2.5
STATION 0
V0
STATION
D0
V2
35
D2
2
At each of these two stations, the mass flow rate is constant,
i.e.
VD
=VD
00
22
where
V
(2-20)
= Linear velocity of feed roller and of the feed
0
yarn passing through
V
= Linear velocity of twisted yarn under thread-
2
line tension
D
= Denier of feed yarn under no tension
o
D
= Denier of twisted yarn under threadline tension
2
The contraction factor is defined as:
C - untwisted yarn length
r
twisted yarn length
(2-21)
constant filament
strain
The denier ratio for constant filament strain as specified
for station
D
2 is:
2
-
D
grams/twistedyarn length
grams/untwisted yarn length constant
(2-22)
+ecold
filament
strain
where ecold is the filament strain in the cold zone at station 2.
Substituting (2-20) into (2-22) we obtain
ecold
V
V= Cr 1
(2-23)
0
36
2.3.4
Cold Zone Tension
Given the tensile strain level of the filaments in the
cold zone, we use the measured constitutive relationship to
determine filament tension.
The corresponding yarn tension in
the cold zone entrance at station #2 is then determined by
resolving the filament tensions in the direction of the yarn
axis by multiplying filament tension by the cosines of local
helix angles.
pressed
Thus the cold yarn tension, T c , is simply ex-
as:
Tc = EcecAf.ENicos~i
(2-24)
1
where
E C = Cold filament extensional modulus
ec = Cold Filament strain (assumed uniform for all
filaments)
Af = Cross sectional area of filament
N i = Number of filaments in it h radial layer
i = ith radial layer helix angle
Equation (2-24) is fully developed in Chapter 3.
2.3.5
Naar
Cold Zone Torque
proposes that yarn torque at the entrance to
the cold zone in the false twist texturing threadline is simply due to components of individual filament bending moments,
filament torsional moments, and filament tension.
Thus he
neglects transverse interfiber stresses and interfiber fric-
37
tion.
We assume that interfiber transverse stresses or inter-
fiber friction do not play a significant role in developing
yarn torque at the cold zone entrance.
However, as is dis-
cussed later, transverse interfiber stresses and friction do
contribute to the high values of incremental torsional rigidity observed in the yarn segment downstream of the cold zone
entrance and in the cooling yarn segment downstream of the
heater.
If the filaments do not exceed their elastic limit
during their traverse of the cold zone, they should not stress
relax significantly before reaching the heater and the cold
yarn twist level should remain uniform.
Actually, there is some stress relaxation of the cold filaments, which results in the yarn slowly gaining twist as it
moves downstream towards the heater.
For simplicity of
analysis, this slight uptwist will be neglected.
For the case of elastic fiber, Platt et al. ( 5 ) have shown
that the components of yarn torque due to fiber bending and
fiber torsion are:
M
Mt cold zone (bending)
EI Rsin
M
GI P cos 3 O
Mt cold zone (torsion)
where
36
p c
EI = Filament bending modulus
GIp= Filament torsional modulus
o
= Helix angle of filament in yarn
R
= Radial position of filament in yarn
38
(2-25)
(2-25)
(2-26)
Pc = Cold twist (radians/twisted length)
The yarn torque due to filament bending and filament torsion
is simply the summation of the individual components of torque from each filament.
The components of individual filament
tension that are perpendicular to the yarn axis are multiplied
by their local radial position in the yarn to determine the
tensile contribution of the filaments to the yarn torque.
This can be expressed as:
Mt cold zone
(tension)
c c fNiRisini
(2-27)
The total torque in the cold zone is then:
zone = EI
t cold
cold zone
Mt
i
Nisin 8+ GI P EN.cos3 8
P c
1
R.
1
+ EcecAf. ENiRisin8i
(2-28)
1
Equation (2-28) is fully developed in Chapter 3.
2.3.6
Hot Zone Tension
The threadline tension at the hot zone entrance is due
to the components of filament drawing forces resolved in the
direction of the yarn axis.
These drawing forces are deter-
mined by the filament draw ratio and the material-system constitutive behavior.
The draw ratio of each filament is de-
pendent on its radial position, on the amount of uptwist
taking place at the heater entrance and on the ratio of yarn
velocity before and after the drawing neck.
39
Brookstein(9)
has shown,
in studies of sequential cross sections through
the necking zone, that there is little opportunity for additional radial migration at this point in the threadline.
How-
ever, the radial migration pattern developed at the cold zone
entrance persists.
Therefore the filament whose position,
upon entering the hot zone, is on the outside yarn layer,
stays on the outside while it is drawn.
From this we deduce
that filaments on the outside of the neck have a greater path
length to follow and therefore draw more than filaments centrally located in the hot yarn.
On the other hand, because of the radial migration which
took place at the cold zone entrance, interchange of radial
position will occur for each filament along its length as it
enters the hot zone.
This interchange assures that each fila-
ment will be subjected to different draw ratios along its
length.
However, the average draw ratio in a long yarn seg-
ment is equal for all filaments.
Figure 2.6 shows an example
of how draw ratio may vary along a yarn length for two different filaments.
Figure 2.6
0H
Filament A
9
Filament B
2:
YARN LENGTH
40
The filament drawing extension in the hot zone can be determined from its path length as is shown in Figure 2.7.
Figure 2.7
/
/
/·
02
I
%_
-
V 3 At
At = Length of yarn entering the neck in time At
V
Let
_
V t
2
At = Length of yarn leaving the neck in time At
V
3
Each (V
· At) yarn length contains (V sec8 ·
2
2
length.
At) filament
2
As this length moves through the hot yarn neck during
At it is drawn to the new length (V sece
3
At).
3
Thus the
filament drawing extension in the neck is simply:
V secO At - V sec
Extension
=3
3
V sec
2
2
At
At
2
2
V secO
13
V sece
2
(2-30)
2
It should be pointed out that filament drawing extension expressed in eq. (2-29)does not include the cold zone strain
referred to in (2-23). For it can be shown that the cold modulus of the filament far exceeds its "drawing modulus" and
thus the levels of filament extension present in the cold
41
zone are about two orders of magnitude lower than the drawing
extensions.
Therefore neglect of cold strain is justified
when determining filament drawing extension.
Having determined filament drawing extension by means of
eq. (2-30), we must now develop information on its constitutive relationship.
And from the latter we will be able to
calculate filament drawing tensions.
Since the constitutive behavior of fibrous polymers incorporates the influence of temperature and strain rate, it was
deemed advisable to measure the local extension behavior under
the same machine conditions as in actual texturing.
The
MITEX False Twisting Apparatus was accordingly used as a continuous extensometer by simply bypassing the pin spindle and
measuring the threadline tension for different draw ratios
and temperatures.
The load-extension data were fit to poly-
nomial expressions through regression analysis and the expression shown below forms the material-system constitutive relationships used in determining filament tensions in the hot
draw-uptwist zone:
Filament Tension = A (Draw Ratio) 2 + B(Draw Ratio) 3
(2-31)
The data on which (2-31) is based, are presented in Appendix 3.
Finally the threadline tension at the hot zone en-
trance can be determined from knowledge of hot zone geometry,
42
filament extensions, and material-system constitutive relations.
Hot zone tension is expressed simply, as:
hot zone
T
= Er Tension.N.cose
oN
i
(2-32)
(2-32)
Substituting (2-3l) into (2-32) we obtain
Thot zone =
(EA(Draw Rationi) + B(Draw Ratio i)
Nicosie
where
3
(2-33)
N i = Number of filaments in ith radial layer
i.
= Helix angle of the ith radial layer
Draw Ratio
Ratioi = Draw Ratio of filaments in the i
radial yarn layer
A,B are experimentally determined material-system
properties.
2.3.7
Hot Zone Torque
The heater is provided in the texturing zone to effect
heat setting of the thermoplastic feed yarn.
In mechanical
terms, this takes place as a result of hot relaxation of cold
zone fiber stresses.
As indicated,the filament stresses in
the cold zone included bending, torsional and tensile stresses.
But as the above mentioned components of threadline torque
are heat relaxed, the line torque cannot be kept constant unless the yarn uptwists, which according to all observations
it does.
This uptwisting incurs some additional filament
43
bending and torsion strains but the resulting stresses are
negligible due to the extremely low hot moduli.
For the case
of the added tensile strains, due to drawing the filament
tensions increase significantly to provide the requisite
threadline tension.
Accordingly, the assumption in our model
is that threadline torque at the heater entrance is based
solely on filament tensile forces.
Thus hot yarn torque can
be expressed as:
Mt hot zone =
LoadNiRi
sinOi
(2-34)
or substituting (2-31) into (2-34)
M
t hot zone
= E(A Draw Ratio
i
+ B Draw Ratio?)
1
NiRisinOi
2.3.8
(2-35)
Calculation of Twist
As indicated previously, there are essentially two levels
of twist in the texturing threadline: the cold zone twist
(which is a fraction of the hot zone twist) and the hot zone
twist.
We assume that the hot zone twist and the cooling zone
twist are equal.
If the hot zone rotational velocity is Wh and the cold
zone rotational velocity Wc then the relative rotational velocities before and after the hot zone entrance is Wh - Wc
and this quantity determines the rate of uptwist at this
44
station according to
Wh - W c
V
h (incremental)
(2-36)
3
where
W h = Angular velocity of hot twisted yarn segment
(radians/second)
W C = Angular velocity of cold twisted yarn segment
(radians/second)
V
= Linear velocity of hot twisted yarn
3
h (incremental) = hot uptwist/hot twisted length
(radians/twisted length)
The hot incremental twist is added to the twist that already
exists in the cold zone due to the angular velocity of the
cold zone
Pc = Wc/V
where
(2-37)
P c = Cold twist (radians/cold twisted length)
V
2
= Linear velocity of cold twisted yarn segment
The cold twist per unit cold twisted length is reduced as the
cold yarn segment is extended by the ratio V /V so that the
2
3
cold twist per unit hot twisted length, Pc/h' is
WV
Pc/h =
V/V
-
2
2
= Wc/V
(2-38)
3
The total hot twist per unit hot twisted length is obtained
by adding (2-36) and (2-38)
45
h = W/V
C3
c =Wh/V
+ Wh
V
(2-39)
3
where
P h = Hot twist per unit hot twisted length
2.3.9
Calculation of Hot Twisted Yarn Velocity
Experimental observation of the twist distribution on
the spindle surface indicates that the twisted yarn in the
texturing zone generally untwists at the last quadrant of the
spindle surface(
From this fact it can be assumed that
the tension in the yarn during untwisting is approximately
equal to the post spindle threadline tension.
The approximate
twist distribution at the spindle is illustrated below.
I
I
D3
Figure
V4D
4 4
4
p.V3LJ3
SP INDLE
The mass continuity requirement is expressed as:
V 33D = V 3 ' D 3 ' = V 44D
where
(2-40)
V = Linear velocity of twisted yarn, before spindle
3
V '= Linear velocity of twisted yarn, at post
3
46
spindle tension
= Linear velocity of untwisted yarn, at post
V
4
spindle tension
= Denier of twisted yarn, before spindle
D
3
D' = Denier of twisted yarn, at post spindle ten3
sion
= Denier of untwisted yarn, at post spindle ten-
D
sion
The friction between the yarn and spindle causes the tension
in the yarn to rise as the yarn progresses downstream around
the spindle surface.
This tension differential and hence
yarn strain differential causes the yarn denier in the last
quadrant of the spindle to decrease slightly.
DI (1 +
3
yarn
) = D
3
Therefore
(2-41)
where
syarn = yarn strain differential across the pin
Now
V D
Then
V'
3
33
(2-40)
= V'D'
33
= (1 +
V
n)
yarn
(2-42)
3
From (2-40) and ( 2-42
V'D' = V D
33
(2-40)
44
47
V (1 +
and
yarn
3
(2-43)
)D' = V 4D 4
3
The cooling twist contraction factor for the cooling
yarn, Crcool, can be expressed as
D'
V
_
-cool
V'
3
(2-44)
3
4
D
4
Substituting (2-44) into (2-43) we obtain
V
V 3 (1 + -yarn
arn)
(2-45)
4
Crool
Again we must make the decision as to which model for cooling
yarn twist contraction factor we should use in the analysis.
Experimental evidence given below indicates that Hearle's
Model for cooling yarn twist contraction fits the experimental
data closer than does the Alternative Model.
Cooling Yarn Twist Contraction
1.60 Draw Ratio 2100 C Heater Temperature
Machine Twist
Measured
Hearle's Model
Alternative Model
50
1.263
1.305
1.220
60
1.396
1.438
1.330
65
1.592
1.601
1.468
80
1.795
1.926
1.745
Experimental evidence presented in Appendix 2 shows that
for a range of steady state operating condition, the tensile
gradient of the threadline across the spindle will result in
incremental yarn strains, ey, of less than 1%.
48
And since the
filament strains in the draw region of the texturing zone are
of the order of 60% to 80%, it follows that for the common
range of draw texturing conditions, neglect of the strain gradient across the spindle will not significantly affect the
calculated value of hot threadline velocity, V .
3
2.3.10
Calculation of Yarn Radii
Most draw texturing feed yarn filaments have circular
cross sections.
When twisted in a yarn structure the fila-
ments generally take the spatial geometry shown in Figure 2.9.
For 34 or 30 filament feed yarns (common apparel yarn structures) there is one central core filament surrounded by three
radial layers of filaments.
It is common practice to model
the structure with 6 filaments in the first layer followed by
12 filaments in the second layer and either 15 or 11 filaments
in the outer radial layer depending on the total number of
filaments in the structure. The cold yarn radius is then seven
times the cold filament radius.
Table 2.1 compares the actual
cold yarn radii with calculated values.
The agreement is good.
When a filament is drawn in the draw texturing process, the
ratio of drawn filament radius to the undrawn filament radius
is
rdrawn
/Pundrawn
rundrawn Pdrawn
where
=
1
draw ratio
p = filament density
49
(2-46)
Figure 2.9
'Arej rniircomncrN
I nupr
paci+
· 18 F'laments
L Loer
12 Filomenfs
x. Capac+jw
Latoer
.ccpaci+tl- 6Filarnents
:i lament
= 5.7
Rodius
x 10
'
YARN STRUCTURE FOR POY POLYESTER
245/30 DENIER
50
a
inch
Rs
4-)
r-I.
H0 0
O
U
r-i
-
rl
r-I
rl
m
1l
r4
r-, r4
rm m
ri
(
H
r-A
r
P
r
r
N
N
N
LO
m
CO
o
o
o
CN
CN
CN
H
Hi
H
H
O
Ln
'.0
LIn
'D
L
O0
mCim
H
0
0 w
o
U)U)
Ln
N
O
auo
34
.4.H
r-
H
N
N
0
0
o0 O N
t
0
O
<
N
O0 o
H
H
O
N
N
N
ci
o'
a
o
o
L
O m
0
0
;1
W
o
o
O"U) o
rro
p4
r
0
P4
I
cI
GO
o
ci
oI
UU
H
U)
CC)
tn
H
0)
*i 0
C
toi
d I
O
0
o*
m
(3
0
O
kD
O
eif
:I
5 0
.0
UUU
U U
O
O
o o
O O
IN N
N
N1
O
0
0
N1
rd
H..
0000
El
a3H
H
0
'iD
*i0 'IO
.O
D
4 4 4 44
tZ
Hl
'10
t
-q H
'
a)
-H
U)
3
O0n0O
'.
Li
O
L~ 0O 00
Li
N cc
'
O
Ln
O
n
.Dd.0
zMdE
51
)
Shealy and Kitson(
show that the ratio of densities for
partially drawn polyester to drawn polyester is 0.972.
the ratio of filament
rdrawn
=
for POY PET according
radii
.986
rundrawn
1
to
Thus
(2-46) is
1
Vdrawratio
Thus we conclude that a good approximation of the hot yarn
radius
is:
rhot yarn = .986
rcold
1
(2-47)
4machine draw ratio
Using (2-47) for various threadlines we obtain the values of
hot yarn radii given in Table 2.1.
These predicted values are
compared to measured values and manifest good agreement.
For the purpose of computation the radial distance from each
filament centroid in a given layer to the yarn center is used
as the radius of that yarn layer.
For example, the radius of
the third radial layer is 6 filament radii, rather than 6 1/2.
The latter quantity represents the outer radius of that layer.
2.3.11
Summary
An analysis of steady state threadline mechanics has
been presented in this section, with a view towards determining steady state levels of threadline torque and threadline
tension, as well as twist distribution over the entire texturing zone.
To undertake calculations based on this analysis,
52
one requires information concerning texturing machine settings
(i.e. spindles speed, feed roller velocity, take up roller
velocity, and heater temperature) and feed stock material
properties.
necessary.
No additional information or measurements are
The treatment of the threadline mechanics incor-
corporates several simplifications and assumptions in accord
with numerous experimental observations:
1.
All filaments are strained equally in the twisted
yarn of the cold zone.
2.
The effect of interfiber friction and transverse
stresses on threadline torque is considered negligible at the cold zone and hot zone entrances.
3.
The friction between yarn and spindle does not significantly affect linear velocities of the threadline
in draw texturing.
4.
Hot zone threadline, cooling zone threadline, and
spindle rotational velocities are equal.
5.
The twist in the texturing zone has two uniform
levels, one for the cold zone, the second for the
hot and cooling zones.
6.
Tension and torque in the texturing threadline are
uniform from the entry roll to the spindle.
7.
Inertial effects on threadline mechanics are considered negligible.
8.
Filaments in the twisted threadline follow ideal
53
right circular helices.
9.
Threadline torque at the entrance to the hot zone is
primarily due to fiber tension.
10. In order to calculate twist contraction in the cold
zone two different models are used, one based on an
averaging over the entire cross section, the other
based on an averaging over the yarn radius.
The
former model (averaged over the entire yarn section)
is used to calculate twist contraction in all other
zones.
In the next section computations based on these steady state
analyses are compared with measured experimental results obtained in draw texturing of partially oriented polyester yarn
(POY-PET).
In a subsequent section we will furnish similar
comparisons for texturing experiments with partially oriented
nylon.
2.4
EXPERIMENTAL STUDY OF STEADY STATE DRAW TEXTURING
2.4.1
Materials and Texturing Apparatus
Polyester partially oriented yarn (POY PET) produced by
the DuPont Company has been used for the experimental study.
The dimensions and properties of the feed yarn are as follows:
Undrawn Filament Denier 245/30
8.17
Undrawn Filament Radius
5.7 x 10
Undrawn Filament Tensile Modulus
4.8 x 105 psi
Undrawn Filament Bending Rigidity
3.97 x 10
54
in
lb-in2
8
Undrawn Filament Torsional Rigidity
1.30 x 10
lb-in2
Filament dimensions and tensile modulus were measured in
the Fibers and Polymers Laboratories at M.I.T.
The bending
modulus was calculated from the tensile modulus based on the
assumption of equal axial tensile and compressive moduli.
The
torsional rigidity (GIp) measured on drawn PET by Mr. J.
p
Donovan of F.R.L. was considered applicable to the current
partially drawn specimen in accordance with Ward's (11) observation that GI does not vary significantly with axial draw
p
ratio.
A laboratory pin-spindle false twist texturing machine developed at MIT (MITEX False Twister) has been used for our
draw texturing studies.
A picture of the MITEX False Twister
is presented in Appendix 4.
In this apparatus the surface
speed of the feed rollers is 0.29 inches per second.
The take
up roller speed is varied in accordance with the required draw
ratio.
The pin-spindle is driven by a motor-belt combination
and the spindle speed is controlled by a Variac Speed Controller and monitored periodically by a General Radio Strobotac.
The spindle speed is varied in accordance with the desired
machine twist.
The heater temperature controller unit is a
standard Rosemount device which is used in commerical texturing operations.
Its accuracy is within ±30 C.
55
The threadline
torque and threadline tension are measured by the MITEX torque
-tension Meter.
dix
Its method of operation is described in Appen-
4.
2.4.2
Results and Discussion
Given the machine settings, i.e. machine draw ratio,
basic or machine twist, and heater temperature, and material
properties,one can use
the computer subroutine "YARN" listed
in Appendix 5 to determine the cold threadline,hot and cooling
threadline twist levels and threadline torque and tension.
Comparisons of the experimental and predicted results are given in Table
2.2 and Figures
2.10, 2.11 and 2.12.
Model
1 in-
cludes the method of radial averaging for cold twist contraction given in section 2.3.2 and Model 2 incorporates Hearle's
method of determining cold twist contraction given in Section
2.3.2.
The results show that there is good agreement over a wide
range of machine twists between the experimental data and the
predicted threadline behavior for both cold twist contraction
models.
reduced.
At machine twists above 70 TPI the agreement is
For example at 80 TPI machine twist, the percentage
differences between the experimental and predicted cold twist,
hot twist, threadline torque, and threadline tension are 24.6%,
29.6%, 2.4%, and 11.9% respectively for Model 1, and 38.8%,
29.6%, 22.8% and 11.3% respectively for Model 2.
Observation
of texturing threadline segments presented in Figure 2.13 in56
.
En
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I.60 raw Ratio
-
06
210'C Heater
3.0
2.0
1.0
0
30
o
20
C
10
.-
0
In
"t,
150
100
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lie
l0
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COLD TWIST
I
,5
50
-
-
55
I
I
60
65
I
80
10
Baosc Twist
experimental
predicted
58
I
I
Figure 2.11
1.60 Droa Ratio
Heate r
190C
3.0
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0
2.0
3-
1.0
0
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a
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.
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65
70
Basic Twist
-
experimental
predicted
59
L
Figure 212
1.6 Ora
a-
Ratio
65TPI Basic
3.0
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o
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0
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E
a
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-
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60
'C
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dicated when machine twist is increased to and beyond 65 TPI,
twisted filaments lose their circular helical geometry.
At 80
TPI the cooling zone segments are continuously torsionally
buckled.
Such buckling invalidates the geometric components
of our assumptions so that the disagreement at 80 TPI is not
unexpected.
We have calculated the root mean square of the percentage
error for threadline cold twist and hot twist, threadline torque and threadline tension for each of these models under a
variety of processing conditions and these values are given
below:
Table 2.3
Model
1
Model
2
Tension
9.3%
23.4%
Torque
12.2%
12.0%
Hot Twist
12.3%
12.3%
Cold Twist
10.9%
16.7%
It is clear that Model 1 provides better agreement between
theory and experiment and so it will be employed in the analysis of unsteady operation of the draw texturing process.
Figures 2.10 and 2.11 (which represent somewhat different
operating conditions) show that as machine twist is increased
while heater temperature and machine draw ratio are kept constant, threadline tension decreases and the threadline torque increases.
This seemingly contrary behavior can be
62
attributed to the increase in local filament helix angles in
the outer layers of the yarn, which reduces the yarn axial
component of filament tension and increases its circumferential component.
As the machine twist increases, the variation of draw ratios in different filament layers in the drawing neck increases.
Table 2.4 presents the draw ratios computed for
each layer of filaments as well as the draw ratio RMS value
for all filaments in a given yarn cross section at a given
machine draw ratio.
Table 2.4
Machine Draw Ratio 1.60 Heater Temperature 2100 C
Machine Twist
Core
1st Layer
2nd Layer
3rd Layer
RMS
45 TPI
1.374
1.428
1.565
1.735
13.9%
50 TPI
1.323
1.394
1.564
1.760
16.0%
55 TPI
1.266
1.358
1.565
1.784
18.0%
60 TPI
1.204
1.322
1.569
1.809
20.1%
65 TPI
1.134
1.286
1.577
1.833
22.3%
70 TPI
1.057
1.251
1.589
1.857
24.8%
It should be noted that even though there is a radial distribution of filament draw ratios.
The weighted average of
the filament draw ratios must equal the machine draw ratio
during steady state operations.
Figure 2.12 shows that temperature of the heater over the
range tested does not greatly affect the threadline proper63
ties.
This follows from the fact that the common range of
texturing temperatures has minimal effect on hot filament
drawing forces.
2.5
EFFECT OF MATERIAL PORPERTIES ON STEADY STATE THREADLINE
BEHAVIOR
If the fiber producer were to alter two material properties
of the texturing, i.e. cold shear modulus and cold extensional
modulus, such modification would affect the threadline behavior during texturing.
The predicted influence of changes in
either modulus, while the other is kept constant is shown in
Figures 2.14 and 2.15
These graphs indicate that if the
shear modulus or extensional modulus is increased, both threadline torque and tension increase, while cold zone twist level
decreases.
Since the hot zone twist was previously indicated
to be a function solely of yarn throughput speed and spindle
speed, the hot zone twist remains unchanged for this case in
which the cold feed yarn properties are modified.
The effect of doubling either modulus on a given threadline
response, i.e. threadline torque, threadline tension, or cold
twist level is presented in Table 2-5.
It can be concluded
that the relative changes in threadline response are minimal
considering the magnitude of either modulus change.
64
Figure
Thread i ne
2.14
vs.loung's 5 Modu\us
Pararmeters
60 TP
D 1.80
t.60
0
I.o
L.
2 1.20
c
50TP
_ - '-- 60
TPI
60Tl
80.0
HOT
SOTP
G
OTPt
COLD
50T Pl
o. 20.0
I.,--o
I
0.0
I
2.0
I
I
4.0
6.0
I
8.0
jouns's Modulus CIo sl)sl
65
Figure
2.15
Threadll ne Pa rameter vs. Torsional
-
I_
60rTT
.0
·
I-
1.80
j
° 1.60
50 TP\
t.O2
.0
830.0
a:
60TPt
60.0
50VP1
I-C"
40.0
w~~rPTP
20.0
I
0.0
I
2.0
t.0
Torsioncl
66
Riqg;dc+y ( 10-8) bln2
Table 2.5
Per Cent
Per Cent
Torque Increase Tension Increase
Machine
TPI
50
Per Cent Cold
Twist Increase
60
50
60
50
15%
15%
5%
5%
-23%
-23%
6%
7%
2%
2%
-10%
-10%
60
Shear Modulus,
+ 100%
Extensional
Modulus
+ 100%
As has been often pointed out in the literature, the cold
tensile modulus is dependent on the draw ratio of the feed
yarn, but the cold shear modulus according to Ward ( 11) is
not.
Therefore changes in cold tensile modulus are easily
accomplished via the fiber producers process control but shear
modulus changes require more fundamental alterations in polymer composition or fine structure.
(We will discuss the
effect of material changes in a later section dealing with
experiments on partially drawn nylon).
Obviously, the simplest modification which can be brought
about in feed yarn properties is accomplished by changing
filament denier for a given yarn denier.
One would expect
that lower filament deniers in such a case, would increase
the tensile contribution to yarn torque in the cold zone.
This direction of change is being developed in the fiber
industry.
Further changes for a given fiber and yarn denier
are easily brought about by altering the filament cross sectional profile, and this method is also under industrial
development.
67
CHAPTER
3
TRANSIENT OPERATION
3.1
INTRODUCTION
It was observed in earlier studies that when texturing
spindle speeds were suddenly altered, the first signs of
twist change in the threadline occurred at the entry to the
heater. (1 2)
It was at this location, during steady state
texturing of PET pre-drawn yarns, that the yarn softened and
the twist rose rapidly from a relatively low cold zone value
to a relatively high hot zone value.
Transient twist changes
introduced at the heater entrance during non-steady spindle
rotation appeared to lock in, remaining essentially unchanged
as they moved with the threadline down towards the spindle.
And a short time after the distrubance one observed that the
transient twist distribution beyond the heater was tilted
downward in the downstream direction for a spindle speed
increase and tilted up in the downstream direction for a
spindle speed decrease.
Seemingly, the threadline achieved
unusually high torsional rigidity after it passed the heater
and locally at the heater entry, it appeared to be torsionally soft.
An experimental study was undertaken to confirm the presence of a torsionally "soft" segment in the threadline at
the heater entrance and of a highly rigid segment at the
68
heater exit and reaching beyond to the spindle.
The results
of these experiments clearly confirm the presence of a soft
segment and a rigid segment in the threadline beyond the
heater.
Further they indicate the presence of an additional
soft segment located at the entry to the cold zone and a
rigid segment consisting of the remainder of the cold zone.
A complementary study was undertaken to determine to what
extent this mode of threadline behavior occurs in the draw
texturing system.
Experimental results indicate that in the
draw texturing threadline there are also regions of torsionally soft material at the cold zone and heater entrance and
rigid segments in the remainder of the cold zone and cooling
zone.
This twist formation behavior during non-steady operation
is significant since the twist level at the spindle at a
given moment is not necessarily the same as the twist level
at the heater entry.
Rather, the twist level at the spindle
at a given moment is equal to that which formed at the heater entrance at an earlier time.
This chapter is divided into three parts.
First, we pre-
sent the experimental observations which are subsequently
used to model transient operation of the draw texturing system.
In the second part we develop two theoretical models
of the transient operation of the draw texturing system along with experimental verification of their validity.
69
Finally the models used to predict threadline response to unsteady machine operation resulting from such causes as unsteady material delivery or material take up, oscillating
spindle speed, etc.
3.2
OBSERVATIONS OF TORSIONAL BEHAVIOR OF THE TEXTURING
THREADLINE
3.2.1
Experiments Using Pre-Drawn PET Yarns
The interactions between processing parameters and
threadline tension of the textured yarn were measured on the
MITEX False Twist Texturing Device, which permitted monitoring of threadline tension through strain gage detection of
the in-line forces acting on the feed roll assembly ( 6)
For these particular tests the machine conditions were, set
as follows, unless otherwise specified:
Feed Speed
1.1 in/sec
Cold Zone Length
Overfeed
1.8%
Cooling Zone Length 5 in
5 in
Temperature 210 C
Twist Direction
S
Heater Length 1.5 in
Pretension
0 g.f.
The machine parameter varied was machine (or basic)
twist, defined as the RPM of the spindle divided by surface
velocity of the take-up roller.
Four levels of twist were
used: 30,45,56, and 60 TPI (basic). The texturing machine
was stopped after operating in steady state at each of the
above conditions and yarn segments from the cold zone and
70
from the cooling zone were affixed to a temporary cardboardclamp system to prevent retraction and/or untwisting.
The
yarn segment was then transferred to a torsion wire instrument, clamped at its top end to the base of the vertical
calibrated wire, and attached to a T-bar clamp at its bottom
end.
This mounting procedure was completed without releas-
ing the twist and without causing further extension of the
Suitable weights were then added
yarn segment being tested.
to the T-bar so as to apply to the yarn that level of tension
which had been recorded during texturing, but without permitting the T-bar to rotate.
Thus, the yarn segment in the
instrument was kept under a tension equal to that of the texturing zone.
At this moment, the angular rotation of the
torsion wire was observed and the yarn torque was calculated.
In all, it was a matter of 30 minutes between the stopping
of the texturing machine and the measurement of yarn segment
torque.
There was no simple way to determine the extent of torque
relaxation which may have taken place during this interval.
But it was observed that, except in one case, the threadline
torque measurements on cold zone segments were within 20%
of the measurements of segments taken from the cooling zone,
with the cold zone values being the lower.
This was not un-
expected since it was likely that the yarn which had been uptwisted over the heater and cooled at constant torque for a
71
period of about 30 seconds, would have encountered sufficient
torsional creep as to minimize subsequent torsional relaxation.
On the other hand, the yarn in the cold zone which
had shorter exposure to the given torque during texturing
and which was not subjected to hot creep should manifest
greater subsequent torque relaxation.
The yarn segment was then uptwisted slightly at the same
tension to permit measurement of incremental torques.
Sim-
ilar experiments were run with incremental downtwisting.
In this manner, it was possible to calculate the torsional
rigidity of the yarn for four different twist levels and for
two different zones of the threadline.
In addition to experiments involving yarn uptwisting at
constant tension, experiments were also run at constant
twist with tension increments added or removed.
resulting torque increments were measured.
And the
Finally, fresh
threadline yarn samples were untwisted completely and a full
torque twist curve was plotted.
This last test procedure
also allowed for measurement of yarn extensions which accompanied untwisting and these data were employed to calculate
twist contraction factors.
The structural data for the threadline observed in these
tests are listed in Table 3.1 and the torsional data in
Table 3.2.
The data show an increase in cold zone twist as
well as in cooling zone twist with machine twist (basic),
72
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although the ratio of twist in the two zones goes from 0.38
to 0.61.
In other words, a higher proportion of twist takes
place in the cold zone at the higher spindle speeds.
Table 3.2 shows the steady state torque values for yarn
segments taken from the cold zone and from the cooling zone.
The latter values are somewhat higher for each condition of
texturing.
As was stated above, torsional relaxation of the
cooling zone specimens is more likely to have occurred during
processing, hence it is logical to select the cooling zone
values as more representative of actual threadline torques.
It is noted that over the machine twist range of 30 to
60 TPI, the torque values increase by about a factor of five,
that is, from 0.4 to 1.9 times 10
in/lbs.
The cooling
zone twist increases by a factor of 2.7, but the cold zone
twist increases by a factor of 4.3.
Threadline tensions are
seen to rise slightly from 30 to 45 TPI machine twist, then
decrease steadily (about 16%) as machine twist increases from
45 to 60 TPI.
This is consistent with the behavior noted by
Backer and Yang
(4)
. The level of cold zone twist manifests a
linear reflection of increases in threadline torque as determined from measurements on yarn segments from the cooling
zone.
This holds up to 56 TPI machine twist (basic).
If threadline tension is relatively constant at machine
twists of 60 TPI the threadline torque remains the same as
at 56 TPI, though the cold twist does increase somewhat.
74
The reason for this flattening of the torque-twist curve becomes evident when one views photographs of threadline configurations(
)
showing the onset of torsional buckling at
60 TPI basic twist for texturing overfeed conditions of 0%.
For the corresponding current tests at 1.8% overfeed, the
torsional buckling at machine twists of 60 TPI basic is even
greater than for 0% O/F.
Figure 3.1, 3.2, 3.3, 3.4, show results of uptwisting
tests on a single yarn segment taken from the cold and cooling zones for the four test conditions listed in Tables 3.1
and 3.2.
The torque plotted in each case for a twist incre-
ment of zero, corresponds to the offline measurement of
threadline torque reading for both cold zone and cooling zone
actual twist values as reported in Tables 3.1 and 3.2.
Again, it is noted that torques for the cold zone yarn segments are consistently below those measured for the cooling
zone segments.
The uptwist-torque values for the most part
vary linearly with the uptwist increments (plotted in radiansper-inch, rather than in TPI).
Upon removal of twist incre-
ments, the relationship is still quite linear, with a slight
hysteresis for the cooling zone segments, but with considerably greater hysteresis for cold zone segments, again reflecting the history of more earlier relaxation in the cooling zone segments in actual processing.
In view of the conclusion that the cooling zone yarn tor-
75
Figure 3.1
150/31
POLYESTERTEXTURED & 210 0 C 1.3% OVERFEED
30 TPI BASIC TWIST
nAMC T'TrIl
1 1 fMV1'1
.LV.l
I c1 1
Uil
.
-
1, U
0
/0
.90
0
COOLING ZONE
RIGIDITY = .12 X
-4
10
IN2 LBS
C,
-J
.380
z
I
O
NAL STIFFNESS
= 7.1
.70
w
C
O
,60
.50
.17 x 10- 5
.40
IN2 LBS
_&--
I
I
.sn
Iv
1.0
2.0
3.0
RAD/INN.
76
4.0
I
I
5.0
6.0
Figure
3.2
150/34 POLYESTER TEXTURED
210°C 1.°% OVERFEED
45 TPI BASIC TWIST
16.7 GRAMS TENSION
2.20
-
COOLING ZONE RIGIDITY =
.24x 10-1
IN 2 LBS
O
2.00
1.80
,)
cn
-J
1.60
z
64
-4
0
1.40
5
w
a
0
1. 20
.BS
-
1.00
.80
0o
!
I
uan
. UU
0.D
1.0
2.D0
3.0
RAD/IN
77
4.0
5.0
I
6.0
Figure 3.3
150/34 POLYESTER TEXTURED
210°C 1.8% OVERFEED
56 TPI BASIC TIST
15 GRAMS TENSION
2.20
2.10
ZONE
GI,= .32 x 10-4
2
IN LBS
2.00
1.90
n
-J
z
1.80
-
I
STIFFNESS RATIO = 1.9
1,70
v
:
cc
IGIDITY
0
1.60
=
.17 x 10- 4
1.50
1.40
1.30
I
LI
0.0
I
,I
I
1.0
2.0
3.0
RAD/IN
78
I
4.0
IN2LBS
Figure 3.4
150/34
POLYESTER TEXTURED a 2100 C 1o
OVERFEED
60 TPI BASIC TWIST
14.1 GRAMS TENSION
2.70
IN2 LBS
2.50
2.30
z
2.10
.L
N2LBS
1.90
1.70
1.50
1.30
I
I
0.0
1.0
I
!
2,0
3.0
RAD/IN
79
4.0
5,0
.I
6.0
ques were the more accurate values, additional incremental
uptwist tests were run on a number of cooling zone segments.
The results of these tests for 30, 45, and 60 TPI machine
twists are furnished in Fig. 3.5 and indicate the spread of
the experimental values observed, as well as the typical
curve selected for Figs. 3.1, 3.2, 3.3, and 3.4.
The slope
of the incremental torque-twist curve is obviously greater
for the 60 TPI machine twist segment than for the 45 or 30
TPI cases, and this is reflected in Table 3.2 as a threefold increase in torsional stiffness over the test range.
The torsional data are summarized in Fig. 3.5, which highlights the tremendous difference between the slope of the
forming torque-twist curve (shown as the solid bars), and
the incremental torque-twist curves (shown as the open bars).
It is also seen that the incremental rigidities vary over the
test range by about 15 times for the cold zone, and only 3
times for the cooling zone materials.
Thus, the data fully
confirm the hypothesis that was put forth on the basis of
observations of tilting in transient twist distributions
after changing of spindle speeds, i.e. that threadline twist
increases imparted at the entry to hot zone are in effect
locked in by the development of high torsional rigidities to
incremental
ptwist over the heater and beyond.
But the
data also reveal that a similar high torsional rigidity to
incremental twist develops right after initial formation of
80
Figure
TfIpRqilNAI
3.5
RFHAVTIP
llF
TFYTIIPRTJG THRFAnI TNF
1.0 x 10 - 5
IN
2
LBS
T
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INCREMENTAL
TORSIONAL
RIGIDITY
m
I
TORSIONAL RIGIDITY
1.5
OF YARN FORMATION
(,
-J
z
a
w
45 TPI-
0
45 TP1
,5
v
MACHINE TWIST (BASIC)
m
30 TPI
20
I
I
I
40
60
80
LOCAL TWIST TPI (NORMAL)
81
Figure 3.6
TORSIONAL ST I FFNESS OF
COOLING ZONE AT DIFFERENT
LEVELS OF 'IOMINAL TW I ST
!
2.8(
-EXPERIMENTAL
....
-
2.6C
BOUNDS
60 TPI,
TYPICAL CURVE
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As
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RAD/IN
82
I
6.0 7.0
the yarn in the cold zone.
Although cold zone rigidities
are somewhat less than the cooling zone rigidities, they are
nonetheless orders of magnitude greater than the cold forming "rigidity".
Likewise, the cooling zone incremental rig-
idity is orders of magnitude greater than the hot uptwisting
-"rigidity". Stated another way, the entries to the cold zone
and to the heater zone are, in effect, dynamic torsional soft
zones in the threadline and any sudden changes which may
occur in threadline torque, for whatever reason, will be reflected in large local twist changes at these entry zones
and negligible changes elsewhere.
And it is to be expected
that twist changes introduced at these points, will be propagated along the threadline with translational movement of
the yarn.
The second series of tests were run on the yarn segments
removed from the threadline.
In these experiments, as was
indicated, the twist of the threadline segment was kept constant while the tension was varied incrementally around the
value recorded as the operating threadline tension.
Incre-
mental changes in yarn torque resulting from these tension
changes were recorded as are reported in Figs. 3.7, 3.8, 3.9,
and 3.10.
The slopes of the curves plotted in these figures
indicate the influence of tension on torque in the cold zone
and cooling zone yarn segments.
There is some increase in
the tension-torque effect as the machine twist is increased
83
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which, in turn, increases both cold zone twist and cooling
But, above machine
zone twist as reported in Table 31.
twists of 45 TPI
(basic), the changes
effect are not consistent.
in the tension-torque
However, it can be noted that the
tension-torque effect for 30 TPI basic machine twist is greater for the cooling zone segment than for the cold zone segment.
And this condition reverses as the machine twist is
increased
to 56 and 60 TPI
(basic).
One expects the tension-torque effect, or the slope of the
torque-tension curve (at constant twist) to depend in the
actual twist in the local yarn segment.
Thus, the larger
slope observed at 30 TPI basic machine twist in the more
highly twisted cooling segment vs. the less twisted cold segment is according to expectation.
The reversal which occurs
at higher machine twists in the comparative levels of cooling
and of cold zone tension-torque effects suggests the possibility of interfilament interactions in the cooling zones
which serve to suppress the torsional response to changes in
yarn tension.
The torque-tension slopes differ significantly from the
cold zone to the cooling zone in a given threadline.
This
fact combined with the confirmed existence of torsional soft
zones at the cold entry and the heater entry suggests that
sudden (and large) changes in threadline tension for whatever reason will result in immediate (slight) redistribution
88
of twists between threadline zones to suppress the torque
differences followed by considerable twist changes at the
soft zones in response to the new uniform (along the threadline) level of torque.
Thus, tensile transients in the
threadline can be expected to cause torque transients as well,
and these will introduce significant changes in soft zone
twisting levels, which will then propagate along the threadline.
Finally, the torque-twist relationship of the cooling zone
segments was determined for the range of untwisting down to
zero torque.
Typical data from such experiments are plotted
in Figure 3.11 where it is seen for the 60 TPI machine basic
twist case (with 91.5 TPI local twist) that the torque-untwist curve (note, for a 5-inch specimen) is fairly linear
from a torque value of about 1.75 x 10-4 in/lbs down to about
0.25 x 10- 4 in/lbs, at which point only one TPI out of ninety
has been untwisted.
The curve then flattens significantly
as the small residual torque is reduced with further twisting
The significance of this behavior will be discussed in Chapter 4 as it relates to product uniformity.
89
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3.2.2
Experiments Concerning Transient Twist, Using
Predrawn PET Yarns
In their photographic study of twist levels during
transient operation of the false twist process Backer and
Yang did not include twist measurements at the entrance to
the cold twist formation zone(
4 ).
In the current study
a photographic analysis was accordingly undertaken to determine how twist changed at the cold formation zone, cold zone,
hot formation zone, hot zone, cooling zone, and post spindle.
zone during transient operation of the conventional false
twist texturing process.
In this case a Bolex 16 mm motion
picture camera equipped with a telephoto lens was used.
The
feed yarns used for photographic twist measurement consisted
of black and white filaments supplied by the DuPont Company.
The yarn (predrawn polyester) was 140 denier with 68 filaments.
To measure local twist at the cold formation zone, a glass
slide was pressed against a relatively friction free roller
to trap threadline twist and prevent it from propagating behind the defined formation point at the slide -- roller 'nip'.
This twist trap assembly was placed slightly downstream of
the feed rollers.
A schematic diagram of the experimental
set up is shown in Figure 3.12.
The machine twist was set either at 30 TPI or 40 TPI and
the system was allowed to reach steady state operating condi-
91
Figure 3.12
MODE
I
I
1.25"
4
GLASS
TWIST TRAP ASSEMBLY
KUULLU;K
MODE II
TRAP ASSEMBLY
FEEI
1.25"
92
TAKE UP
tions.
The machine twist was then step changed by 10 TPI to
either 40 TPI or 30 TPI depending on the previous twist level.
Motion pictures of the threadline were taken at different
positions so that twist levels could be determined as functions
of time ( after disturbance) and position.
These pictures
were taken at the following positions:
IN COLD ZONE:
Cold Zone Entrance
3.50 Inches Past Cold Zone
6.88 Inches Past Cold Zone
IN HOT ZONE:
Heater Entrance
Midway Through Heater
Heater Exit
IN COOLING ZONE:
Immediately After Heater
.50 Inches Past Heater Exit
3.00 Inches Past Heater Exit
7.37 Inches Past Heater Exit
IN POST SPINDLE ZONE:
7.00 Inches Past Spindle
Graphs of twist versus time at different positions of the
threadline after a step change in spindle speed are given
in Figures 3.13, 3.14, 3.15, 3.16, 3.17, 3.18, and 3.19.
Figures 3.13 and 3.14 show that there is an apparent time
lag in the cold twist redistribution during transient operation.
Twist levels at the entrance to the cold zone manifest
immediate change after the spindle speed is changed. Twist
93
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levels downstream
of the entrance to the cold zone appear
relatively unchanged at first.
About 6 seconds later the
twist level 3.5 inches downstream of the entrance changes;
the twist level 6.88 inches downstream of the entrance changes
soon thereafter.
The time for a sudden twist change at a
given threadline position in the cold zone is plotted against
the downstream distance
of that position in Figure 3.20.
The slope of the line connecting the experimental points
approximates the value of the nominal yarn throughput speed.
Figures 3.17 and 3.18 show this same type of twist behavior
downstream of the heater.
Earlier observations of tilting threadline twist distributions following upon sudden changes in spindle speed
provided the basis for the hypothesis that torsional rigidity
of the conventional texturing threadline is significantly
lower at the at the heater that beyond in the cooling zone.
The existence of the "soft" torsional zone at the entry to
the heater has been confirmed but it has been also shown that
the entry to the cold zone in conventional texturing is likewise a torsional soft zone.
Torsional disturbances in the
threadline are evidenced primarily as twist changes at the
soft zones and these changes then propagate downstream with
yarn movement.
The formation rigidities of the texturing threadline essentially reflect the rigidity of the soft forming zones under
101
Figure 3.20
I..
A
B
.25
z
w
I-
K
E,
w
.1
I.-
"
i
"
"
m753
v
=
ISEC
0.0
0.0
6.0
2.0
4.0
6.0
.
D
.2
z
. Z-
.1
v = .707 IN/SEC
0.0
0.0
2.0
!
!
4.0
6.0
V = .
I
POSITION, INCHES
0.0
2.0
4.0
6.0
POSITION, INCHES
TIME FOR A SUDDEN CHANGE IN TWIST AT A GIVEI MACHINE POSITION
AFTER A STEP INPUT
A.
B.
C.
D.
STEP CHANGE FROM 40-30 NOMINAL TPI OBSERVED IN
STEP CHANGE FROM 30-40 NOMINAL TPI OBSERVED IN
STEP CHANGE FROM 30-40 NOMINAL TPI OBSERVED IN
STEP CHANGE FROM 40-30 NOMINAL TPI OBSERVED IN
COLD ZONE
COLD ZONE
COOLING ZONE
COOLING ZONE
NOTE: ItOMINAL THROUGHPUTSPEED IS .734IN/SEC
102
the conditions of local twist insertion.
The twist response
of cold zone and cooling zone segments to incremental changes
in spindle speed reflects the very high incremental torsional
rigidity of these threadline segments.
The obvious question to be asked concerns the reasons for
the sudden stiffening of the threadline a short distance beyond the two entry zones.
One can attribute these rigidity
differences to the variation in twisting deformation modes at
each of the soft zones and in segments which lie downstream
of these soft zones.
Observations of dynamic twist formation in larger models
indicate that many filaments approaching the twist triangle
apex are already twisted around their axes and sometimes around
neighboring pairs.(13)
They are then wound onto the newly form-
ed end of the yarn, with little additional twisting observed
thereafter.
After the twist is inserted at the cold zone
entrance, interfilament friction and transverse stresses cause
the yarn to behave like a helically anisotropic solid rod with
subsequent high torsional rigidity.
This yarn segment can now
accomadate relatively large threadline torque variations with
very small changes in threadline twist level.( 1 4)
The situation at the uptwist zone at the heater involves
sudden stress relaxation or softening of the tensioned filaments
as might be expected from thermomechanical studies.
ment
The require-
of constant threadline torque in presence of this stress
relaxation results in a cranking up of the twist at the heater.
103
As the new hot twist level is being reached, the lateral forces
due to filament tensions and local curvatures will also reach
a new high level.
And this increased interfilament pressure
accompanied by thermal softening will result in lateral
compressive creep and in growth of contact areas between filaments.
Higher friction and interfilament shear stresses will
then result in higher incremental torsional rigidities.
Experience thus far suggests that it will require extensive
additional experimentation
to verify these hypotheses.
An
alternative approach is to model the yarn on the basis of these
various hypotheses, then to predict threadline behavior on the
basis of these models.
Thwaites14
has taken this approach in his theoretical
analysis of the torsional behavior of the false twist threadline.
3.2.3
Experiments Using POY PET Yarn
After experimental
characterization of the torsional
behavior of the conventional false twist threadline it is
necessary to do the same for the draw texturing threadline.
Accordingly, partially oriented yarns (POY PET) supplied by the
Du Pont Company were used for the study.
The POY PET consists
of 30 filaments and is 245 denier with a prescribed draw ratio
of 1.60.
The results of the torsional rigidity study are given in
Table 3.3 and in Figures 3.21, 3.22,
and 3.23.
Figure 3.21
shows that for a fixed machine draw ratio and heater temperature
104
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§
Figure 3.21
INCREMENTAL TORSIONAL RIGIDITY
DRAW TEXTURED YARNS
245 DENIER YARN
TEXTURING CONDITIONS:
1.60 DRAW RATIO
210
C.
4.0
3.5
.-rl
4
COOLING
3.0
*~~~~:~~~0
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Il
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50
I
60
I
65
I
70
MACHINE TWIST, TPI
106
I
80
Figure 3.22
INCREMENTAL TORSIONAL RIGIDITY
DRAW TEXTURED YARNS
TEXTURING CONDITIONS:
245 DENIER
65 TPI BASIC TWIST
1.6 DRAW RATIO
_
_
CN
__
4.0
l
3.5
>o
3.0
COOLING
-
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H
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all
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COLD
U]-
1.0
-
0.5
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I
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1900 C.
2100 C.
HEATER TEMPERATURE
107
I
2300 C.
Figure 3.23
INCREMENTAL TORSIONAL RIGIDITY
DRAW TEXTURED YARNS
TEXTURING CONDITIONS:
245 DENIER
65 TPI BASIC TWIST
2100 C HEATER
4.0
U,
CN
u3
3.5
O
._-OLING
0l
3.0
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2.5
H
H 2.0
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0 1.0
0.5
0.0
I
1.57
I
1.60
MACHINE DRAW 'RATIO
108
I,
1.64
increases in machine twist cause the incremental rigidity
of the cold zone yarn segments to increase.
However, the
incremental torsional rigidity of segments taken from the
cooling zone peaks at 60 TPI machine twist and then drops
as machine twist is increased.
The behavior of the cooling
zone segments is attributed to the observed torsional buckling of the cooling zone segments at high machine twist
levels (Figure 2.13)
Figure 3.22 shows that as the heater
temperature is changed there appears to
sional rigidity at 2100C.
be a maximum tor-
This corresponds to the maximum
cooling zone twist observed when the POY PET is textured at
210°C, as shown in Table 3.3.
Lastly, as the machine draw ratio increases, the torsional
rigidity of the cooling zone segments increase as seen in
Figure 3.23.
For the cold zone segments, the torsional
rigidity reaches a peak at 1.60 machine draw ratio.
This
corresponds to the peak in twist level for this machine
draw ratio.
3.2.4
Experiments Concerning Transient Twist, Using
POY PET Yarns
The cold zone twist distribution was photographed as
before for the conventional false twist texturing threadline.
The machine parameters were set as follows:
109
Post Spindle Length
9.00 in
Cooling Zone Length 7.00 in
Heater Temperature
2100 C
1.25 in
Machine Draw Ratio
1.60
Cold Zone Length
Hot Zone Length
6.00 in
Pictures of the threadline twist levels were taken at a
position one inch downstream of the cold zone entrance and
five inches downstream.
Twist observations are recorded in Figure 3.24 and 3.25.
The twist level one inch into the cold zone appears to undergo
a rapid change, a short time after the step increase in spindle
speed.(Fig. 3.24)
At five inches into the cold zone there is
a definite time lag after the step increase in spindle speed
before the twist level begins to change significantly.
Difficulties were encountered in repeating the above
experiments for the hot zone and the cooling zone. For with the
texturing machine operating in the same twist level as that
used in measuring cold twist, the hot and cooling twist levels
were too high in the "semi-welded" yarn to permit measurement
of twist.
To overcome this difficulty, a lower steady state
machine twist level was employed and the spindle speed was
suddenly reduced.
The hot and cooling zone transient twist
distribution was then observed.
The machine parameters in
the latter experiment were:
6.0 inches
Cold Zone Length
Cooling Zone Length
110
15.0 inches
N
(1)
.rtj)
rLI
I-
0
Se
0
7H
I:
U)
10
Qm
0
4.
I
LU
I
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II
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I
i
I
!
I
I
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-
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laa
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o
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w
Hot Zone Length
1.25 inches
Post Spindle Zone
9.00 inches
Heater Temperature
210
Machine Draw Ratio
1.60
C
Motion pictures of the threadline twist levels were taken
at the beginning of the heater, at the end of the heater,
immediately after the heater, and nine inches from the heater
in the cooling zone.
Figures 3.26
from the twist measurements.
and 3.27 show the results
Just as occurred in the cold
zone the twist level at the heater entrance drops off immmediately after the spindle speed is reduced while there is
a definite time lag for the twist to drop off nine inches
into the cooling zone.
It should be noted that local twist
at the downstream end of the heater and at the entrance to
the cooling
zone, also respond to the step drop in spindle
speed, with no clear evidence of a time lag.
Finally
Figure 3.27 shows that the twist level across the heater and
through the cooling zone is not actually uniform at steady
state.
This slight amount of uptwisting is probably due to
further relaxation of filament tensile forces.
Also at the
heater-cooling zone interface there is a slight steplike
uptwist of about one turn per inch.
Backer and Yang
(4)
have identified this behavior for conventional texturing
threadlines. Thwaites (14) analytically describes this uptwist as that which causes a cooling zone incremental torque
equal to the threadline torque.
113
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115
3.3
ANALYSIS OF TRANSIENT OPERATION
3.3.1
Introduction
The analysis of steady state operation as developed in
Chapter 2 was based on the fact that the threadline tension
and threadline torque are essentially uniform along the texturing zone and that during transient operation there are no
transient material or twist buildups in any zone of the process.
During steady state operation it was shown that there are
essentially three levels of twist between the feed rollers and
the take up rollers: the cold twist level, the hot or cooling
twist level, and the post spindle level.
Transient operation generates material buildups and twist
buildups with respect to time in different zones of the texturing system.
However, the threadline tension and thread-
line torque at any given instant are considered uniform along
the texturing zone during transient operation, as well as in
steady state operation.
This section presents two models which are used to calculate
threadline response to transient machine operation.
Each model
is used to predict cold, hot, cooling, and post spindle twist
levels as well as threadline tension and threadline torque.
The first model is based on the physical simplification that
uniform twist levels persist during transient operation in the
cold, hot, cooling, and post spindle zones.
The second model
provides for non-uniform twist distribution in the cold zone
116
and in the cooling zone and it formulates these distributions
according to experimental observations discussed in the previous
section.
The numerical results derived from these two models will be
compared to experimental data to determine the effectiveness of
the models.
After comparison is made, a parametric study is
reported showing how unsteady machine behavior affects the transient operation of the draw texturing process.
3.3.2
Method of Solution
During steady state operation of the draw texturing process
threadline tension and threadline torque are considered uniform
in the zone between the feed rollers and the spindle.
Since
inertial effects are indicated to be negligible, threadline
tension and threadline torque can also be considered uniform
along the texturing zone during transient operation.
We can
now determine the material-system constitutive relations, yarn
geometry, and system compatibility at any yarn cross-section,
and use these relations to predict threadline torque and
thread-
line tension.
During steady state operation neither the number of turns nor
the amount of material in any threadline zone changes with
respect to time.
Therefore in each zone, i.e., the cold zone,
hot zone, cooling zone, and post spindle zone, the input turn
flow rate is equal to the output turn flow rate and the input
117
material flow rate equals the output material flow rate.
During transient operation these flow equalities no longer
obtain and the number of turns and amount of material in any
zone generally varies with time.
Transient analysis of the draw texturing process must include
material balances and turn balances for each defined zone of the
texturing threadline(i.e. cold, hot, cooling, and post spindle).
To complete the analysis,these balances are coupled with the
requirements of threadline tension and threadline torque uniformity in the zone between the feed rollers and spindle.
In
this section,the relations which describe the transient threadline mechanics will be expressed in functional form. We will
then show how these functional relations are used to predict
threadline tension, threadline torque, and local twist levels
during transient operation.
In subsequent sections detailed
expressions will be formulated.
A block diagram which shows how the variables in the draw
texturing analysis are related to each other is presented in
Figure 3.28.
For each block there is an equation developed
in the text which relates the variables according to threadline
mechanics.
118
Figure 3.28
RELATIONSHIPOF VARIABLES IN DRAWTEXTURINGPROCESS
V0o
FEED ROLLERS
ICOLD
COLDZONE
I
I
SPINDLE
I
I~~~~~
HOT ZONE
II
i
I
I~~~~~
COOLING ZONE
I
I
IPOST SPINDLE ZONE
I
II
MATERIAL
BALANCE
TURN
BALANCE
TEREADLINE
TORQUE
THREADLINE
TENSION
PC = TWIST/UNIT LENGTH AT UPSTREAM END OF COLD ZONE
j
TWIST/UNIT
LENGTH AT DOWNSTREAMEND OF COLD ZONE
TWIST/UNIT
LENGTH OVER HEATER AND UPSTREAM END OF COOLING ZONE
Ph
Ph = TWIST/UNIT LENGTH AT DOWNSTREAMEND OF COOLING ZONE
Pps TWIST/UNIT LENGTHIN POST SPINDLE ZONE
V0 - FEED ROLLERSURFACEVELOCITY
V 2 = LINEAR VELOCITYOF YARNAT COLD ZONE EXIT
V3 = LINEAR VELOCITY OF YARN AT HOT ZONE EXIT
Vb- LINEAR VELOCITY OF TWISTED YARN AS IT ENTERS SPINDLE
ec
STRAIN OF FILAMENTSIN COLD ZONE
th
RADIAL YARNLAYER IN HOT ZONE
Dri= DRAWRATIO OF FILAMENTSON i
Wc
ANGULAR VELOCITY OF YARN IN COLD ZONE
Wh
ANGULAR VELOCITY OF YARN IN HOT ZONE
WS
=
ANGULARVELOCITYOF SPINDLE
*The numbers in parenthesis refer to equations in text
119
I
I
LIST OF SYMBOLS
A,B, = Hot Moduli of Drawing Coefficients
Ail
A
Ai3 = Defined Coefficients
AN. = No. of Filaments in Hot Zone ith Radial Layer
1
BN. = No. of Filaments in Cold Zone ith Radial Layer
Cr
= Cold Contraction Factor (Alternative Model)
Cr
= Hot Contraction Factor (Hearle's Model)
Cr. = Contraction Factor at Twist Level P. (Hearle's Model)
I
-
Cr
= Contraction Factor at Twist Level Pps(Hearle's Model)
Crset = Contraction Factor in Set Zone (Hearle's Model)
Dr i = Draw Ratio of Filament in i
Radial Layer
Ec = Cold Young's Modulus Cross Sectional Area of Filament
ec = Average Tensile Strain of Filaments in Cold Zone.
EIfiber = Cold Bending Modulus of Fiber
Fo,F1lF
2 ,F 3 ,F 4 ,F5 1 F6 ,F 7
= Defined Coefficients
GIfiber = Cold Torsion Modulus of Fiber
120
G1 ,G2 ,G G3 ,G 4 ,G5 ,G6 G7 = Defined Coefficients
Lc = Cold Zone Length
Lh = Hot Zone Length
L
ps
= Post Spindle Zone Length
L s = Length of Set Zone
P
= Twist in Cold Zone, (Radians/Inch)
Ph
=
Twist in Hot Zone, (Radians/Inch)
Pj = Twist at Downstream End of Cold Zone (Radians/Inch)
Pps = Twist in Post Spindle Zone (Radians/Inch)
Ps
=
Twist at Downstream End of Set Zone (Radians/Inch)
Q1,Q2'Q3 = Defined Coefficients
R.
ic
= Radius of ith Radial Layer in Cold Zone
th
Rih = Radius of i
Radial Layer in Hot Zone
SecO3i = Secant of Hot Zone Helix Angle at i
SecO2i
Radial Layer
= Secant of Cold Zone Helix Angle at it h Radial Layer
t = Time, Seconds
Vb = Velocity of Hot Twisted Yarn at Spindle Entrance
121
V 0 = Feed Roller Linear Velocity
V 2 = Linear Velocity of Cold Twisted Yarn
V 3 = Linear Velocity of Hot Twisted Yarn
V 4 = Take Up Roller Linear Velocity
W c = Angular Velocity of Cold Zone Segments
Wh = Angular Velocity of Hot Zone Segments
W
= Spindle Speed and Angular Velocity of Cooling Zone
Segments
X1,X2,X3,X4,X5,X6,X7,X8 = Defined Coefficients
Y1 ,Y 2 ,Y3 ,Y4 = Defined Coefficients
Z,ZlZ
2
= Defined Coefficients
122
In Chapter 2 it was shown that the yarn tension at the
cold zone entrance can be expressed as
Tc = F 1
(ecP c)
(2-1)
Differentiating (2-1) with respect to time we obtain
d Tc = G
=c
dt
G
e
d P
- c
dt
c
(3-1)
dt
Yarn torque at the cold zone entrance was expressed in
Chapter 2 as
Mtc = F 4 (ec,Pc)
(2-4)
Differentiating (2-4) with respect to time we obtain
ddtdt/
d Mtc = G(dec
,
d Pc
(3-2)
At the entrance to the hot drawing zone it was shown in
Chapter 2 that
Th = F 5 (V2 VP3
c) Ph
(2-5)
Taking the variation of filament draw ratio in the yarn cross
section into account, we can express (2-5) more simply as
Th = F (Dri,Ph)
*
(3-3)
The symbols F,G,X,Y,Z indicate various functional expres-
sions which are developed later.
123
And likewise yarn torque at the hot zone entrance is expressed
as:
Mth= F(Dr i ,Ph)
(3-4)
Both (3-3) and (3-4) are differentiated with respect to time
to obtain:
(3-5)
d Th
dt
dt
\dt
Dri
d Mt = G 6
dt
d Ph
(3-6)
dt
dt
Satisfying the requirements of threadline torque and threadline tension uniformity, we can equate (3-1) and (3-5) as
well as (3-2) and (3-6) to obtain:
0
Gd
e,
dt
= G2d
d P
-
dt
ec , d P
G
d Dr., dPh
dt
-
at
dt
dt
G6 d Dri, d Ph
dt
(3-7)
(3-8)
dt
Equations (3-7) and (3-8) represent generalized threadline
coupled force differential equations
Section 3.3.3.1.
They are developed in
They are 2 equations with 4 unknowns.
The
analytical relationships required to complete the analysis
are developed from the material balance relation and turn
balance relation for each zone in the texturing threadline.
124
In Section 3.2.4 it was reported that the twist distributions
observed
in both the cold and cooling zones of the threadline
operation were not uniform with respect to position.
One of our
modelsfor transient operation is based on these observations of
non-uniform twist distributions.
siplification
Another modelis based on the
that the twist levels are uniform throughoutzones
during transient operation.
Cammn
to both models is threadline
behavior
both in the hot (i.e. over the heater) and the post spindle zones.
For it has been observed that twist distribution during transient
operation is the same as for steady state operation across the heater
and post spindle zones.
The material balance for the hot zone will be fully developed
in Section 3.3.3.2 but it can be functionally expressed as
dPh
V2
-Xl(Ph'PC' Dr.,
d Dr.
V3
(3-9)
Likewise, the turn balance for the hot zone which is to be developed
in Section 3.3.3.2 can be functionally expressed as
dP
dWt
hX2
FWc,PC' V2 ' Ph'V
(3-10)
The post spindle analysis given in Section 3.3.3.2 dem strates
that
dP
p_s
dt
x 3 (Pps, PWpsVb)
(3-11)
sps
125
and
Vb= X4(Pps' WPs'
where
(3-12)
lePS)dt
Vb = linear velocity of twisted yarn as it enters spindle.
Since we assume that the cooling and hot zone segments rotate
at the same angular speed
as the pin spindle (Wh = W
= W s ) equations
(3-7), (3-8), (3-9), (3-10), (3-11), and (3-12) can be combined to
yield
5 differential equations with 10urlawns; Pc,
phDr ,,ecVb
v3,v 2, Pp, P, and W . The analysis can be carpleted
onsidering
the material balances and turn balances in the cold and cooling
zones. To deal with the turn balances, we resort to the two models
for twist distribution as mentionedabove.
3.3.2.1
MODEL 1: Flat Twist Distribution
Model 1 is based on the smplifying
assurption that the twist
distributionis uniform flat in the cold zone and in the hot and
cooling zones during transient operation.
equal at all times.
The latter twists are
The material balance for the cold zone developed
in Section 3.3.3.3 shows that
Vz = X 5 (ec, Pc
dPc , d e c )
dt
(3-13)
dt
The turn balance for the cold zone developed in Section 3.3.3.3 shows
that
126
dP
c
dt
The material
(3-14)
X (WcPc' V)
linznedeveloped
balance for the
in Section
3.3.3.3 shows that
dP
X7 (Ps , V 3 , V b
dt
Ph)
(3-15)
where Ps = turns/twistedlength
in cooling zone.
The turn balance for theoolig
zone is expressed as
dP
dt
= X 8 (PhV
3
,Vb'P
) s
(3-16)
Lastly, by definition
Ps
=
Ph
(3-17)
In summary, equations (3-7), (3-8), (3-9), (3-10), (3-11), (3-12),
(3-13), (3-14), (3-15), (3-16) and
of which 10 are differential
P
e, V,2
V3 , Vb, ec,
(3-17)
equations
represent
11 expressions
with 10 unknowns;PPhPs,
Dr.
After considerablemanipulationthese equations can be -rduced to
the following:
dP
dt
z1
1 [Pc, Ph' ec Dri,
127
Pps
(3-18)
dP
-Z2[Pc
Ph' ec' Dri, P
(3-19)
dt
de
c
= Z3[Pc'Ph
eC,'Dr.i PP
(3-20)
dt
d Dr.
-1
= Z 4 [Pc Ph' e
ps]
Dri
(3-21)
dt
dP
PS.= Z5 [PC, Pht et Dr,
P S
(3-22)
dt
This system of non-linear ordinary differential equations is
solved numerically by a digital computer.
The solution technique
is described in Section 3.3.4.
After obtaining Pc, Ph' ec, and Dr.
as functions of time,
e
substituted these values into (2- .1),(2-4), (3-3) and (3-4) to determine
threadline tension and threadline torque at any instant during
transient operation.
3.3.2.2
Model 2: Tilted Twist Distribution
Model 2 is based on the assumption that the twist is not
uniform, along the cold zone nor along the cooling zone.
An approxi-
mat kinematic relation (twist transport equation) is fonmulated which
relates the twist level at the downstream end of either zone to the
corresponding twist level at the upstream
128
portion of that zone.
The
force, material
upstream twist levels are determined by the arriate
and turn balances.
The twist transport equations for the cold zoneand cooling zone
are developedin Section 3.3.3.4 and are expressed functioally as
d P.
3
dt
V2]
(3-23)
Ph' Vb]
(3-24)
Pj,
=X9[Pc,
and
dPs
= X10[Ps,
dt
where P = twist/unit length at downstreda end of cold zone
P's= twist/unit length at dmnstream end of cooling zone
The material balance for the cold zone developed in Section 3.3.3.4
showsthat
V2 =X 1 (ec P
P
dP
dP
d.e
dt
dt
dt
]
(3-25)
Likewise, the turn balance for the cold zone developed in Section 3.3.3.4
shows that
dP.
dP
=dt
X1 [W Pc P
dt
12 c
c
'
2
dt
1
(3-26)
The material balance for the cooling zone shcws that
dP'
dt
s
X13 (h
dt
Ph' P;' V3 Vb)
129
(3-27)
Finally, the turn balance for the cooling zone can be expressed as
d .P
d Ph
= X14
dt
In sumnazyeuations
(3-28)
Ph' V3 ' Vb]
P
dt
(3-7), (3-8), (3-9), (3-10), (3-11), (3-12),
(3-23), (3-24), (3-25), (3-26), (3-27) and (3-28) represent a system
of 12 differential equaticns with 11 unkrans;
W V22v
After cnsiderable maniplatian these
e, , and Dr..
, Vb
Pcp' i' Ph ; PS'
can be reduced to the following:
dP
'P
Y1 [Pc' Pj,
dt
P s
'
ec,, r
(3-29)
P
e, Dr.]
(3-30)
d P.
dh =-Y2 [Pc'
P,
dt
h', P,
de
Y3 [PC Pj' Ph' P'
dt
at
Dri]
Pps e
(3-31)
d Dr.
-=_Y4Pc
d P.
'
= Y5[Pc' Pj
Pj
Ph' PS
P'
Pp,
s = Y6pC Pi P,,P'
P'
Ph'
i]
ps e
e,
Dri]
(3-32)
(3-33)
dt
d P'
dt
130
, D]
]~IelD
(3-34)
d P
PS= Y[P
7 C Pi' P'
dt
Ph Ps PPs
This system of nan-linear ordinary differential
numerically by digital carputer.
equaticns is solved
The solution technique is described
in Section 3.3.4.After btaining
of time
(3-34a)
e,
Dr.L
C -.
Pc Ph'Drias
functions
we substitute these values into (2-1.), (2-4), (3-3) and (3-4)
to deteine
threadline
torque and thradline tensions at any
instant during transient operation.
131
3.3.3
Transient Threadline Mechanics
3.3.3.1
General Tension & Torque Relationships
In Chapter 2 the yarn tension at the hot zone entrance
was derived as*
Th = ANO
(A
+ AN 11 · (A
2
+ B
Dr 30)
Dr 2 + B
Dr 3)
Dr
-O
-
12
l+P Rlh
2
+ AN2
*
(A
Dr
+ B.
Dr 3)
0
1
1+PhR 2 h
+ AN 3 '
3
(A
Dr
-3
+ B * Dr3 )
-3
.
1
(3-35 )
v1+P hR3h
3h
Equation (3-35 ) is now differentiated with respect to time
to obtain.
*Note: Since most yarns which are draw textured are 3 layer
multifilament yarns and the yarns used for experimental study
are such, the analysis will be formulated to accommodate this
type of yarn.
Simple arithmetical changes could be made if
this were not the case.
132
dTh
dt
= AN0
· (2,A-Dr0 + 3,B-2Dr) dDrO
dt
+ AN
idDr
2
3.B
dt
1
222 1/2
(l+PhRlh
+AN2*
2)
(2.-A-Dr+ 3B'*Dr
·
dDr2
2
dt
(l+P 2 R 2 )1/2
h 2h
+AN
AN 2+
2
. (2-A.Dr3 + 3-B*Dr
· 2 32
(l+P 2 R 2
h 3h
dDr 3
1/2
)/2
-Ph AN(A.Dr + BDr)
dt
2
Rlh
(l+PhRlh)3" 2
2
+
AN 2
+ BDr
(A
+2 AN[A~r
2B.Dr
3
2
2h
(1+PhR2 2 h)3/2
+AN3(A.Dr + BDr 3)
3h
2 2 )3/2
dPh
( 3-36 )
dt
1+PhR3h
To simplify equation (3-36) we define the following
Fo- AN0 (2ADr0 + 3BDr)
( 3-37 )
F1
2)
AN
- 1
1 (2ADr
- l + 3BDr
3 r )
( 3-38
)
2
- AN 2 (2ADr2 + 3BDr2 )
( 3-39
)
3
-
AN 3 (2ADr3 + 3BDr2 )
( 3-40
)
1
133
-P . F·
-%.
2
N1 (A,Dr1 + BDr
3
2
R2
), Rh
2 2 3/2
(1+PhR1)
L
+AN 2 (A*Dr2 + B Dr 2 )
-2
.
2
R2h
2
2 2
3
3/2
+AN3 (ADr 3 + B-Dr3)
(l1+PhR
3 )2
Substitution of ( 3-37), ( 3-38), ( 3-39), ( 3-40) and (3-41 )
into ( 3-36) gives
dT h = F
dDr0
at
+ F
dDr
dDr2
+ F +
tt
+F
dt
dDr3
dt
dPh
( 3-42)
dt
In Chapter 2 yarn tension in the cold zone entrance was
derived as
T
c
= E e
c c
+ BN3
2
2
1/2
L(1+PR212
L. c c
E
BN2
+2R2
1/2
(1+P
2 )
3
(1+P
cRI
c 3c
where
+
BN
( 3-43
1/21
c = Cold tensile modulus x Area of filament
Equation (3-43 ) applies during both transient and steady
state operation.
Therefore if we know the cold filament
134
)
strain and the cold twist at any time, the threadline tension
Equation ( 3-43 )
can be determined therefrom.
is different-
iated with respect to time to obtain
d(T c)
dt
= E
BN1
c
2 21/2
(i+P R
+ BN3
/
BN.2
(1+P2R 2 ) 1 /2
c
dec
(1+P2R2 )1/
dP
+
dt
BN2 Pc R2
c
+
dt
2
c
2c
(1+P2 R 2 )3/2
c 2c
)
(3-44 )
+
(1+Pc R3c
3 )
To simplify equation (3-44 ) we define the following
F
- E
+ BN2
BN1
2 2
1/2
(+PcRlc)
(l+P2R2c)1/2
c 2c
+ BN 3
(3-45 )
223 )/2
1/2
(1+PR
c · 3c
F7 - E e P
7cc
BN
R2
BN 2 · R2c
22lc 3/2+ (1+P
2 R22c3/2
+
(l+P2
)3/2
I(+PR )
1
1
c lc
2
BNR 3c
+
BN3
2 2
(1+P2R
c 3c
where
c 2c
(3-46 )
) 3/2
I
BN .= Number of filament in i th radial layer in the cold zone
1
135
To obtain:
dTc = F dec + FdP
dt
6dt
(3-47
)
/dt
In Chapter 2,yarn torque at the hot zone entrance was derived
as
R2
th
AN 1 (ADr
+AN
2
2
2
+ AN2(A D r
+ B.Dr3).
hRlh
2 2 1/2
(1+PhRlh)
PhR 2
h 2h
3
+ B'Dr2
22
1/2
l+PhR2h
2
2
3
+ AN'33 (ADr
+ BDr
) .h PR 3h
-- 3
2r33
( 3-48
)
(1+P2R2 )1/2
3h
Equation ( 3-48) applies during transient and during steady
state operation.
Therefore,given the individual draw ratios
of the filaments and the hot twist at any time, we can determine the corresponding threadline torque.
Equation ( 3-48) is
now differentiated with respect to time to obtain.
d(Mth) =AN
(2-A*Dr + 3BDr
2
1
1
dt
2
dD
PhRlh
(l+PR2 2
hlh
1/ 2
136
dt
+AN1 AN
[L-1
+ DBr1)R2
2
PhRlh
1/2
d
dPh
(1+PhRlh)32
N (2.aDr 2 + 3
2.Dr
P
R
2h
(1+PR2h)
+ AN2 A.Dr2 + BDr 3) R2h]
2h
137
2
1/2
dt
22
-h
2h
PhR2h
+ AN3(2-ADr
3
3[
!-3 + 3BD
_dt
dt
+ AN
3 FA-Dr + BDr 3 )
dDr3
Ph3h
(l+P2R3h) /2
)
2B'Dr3
3
dt
h 3
1
dPh
-
( 3-49)
dt
To simply Equation ( 3-49) we define the following
1
= AN1 (2A .Dr + 3BDr
PR 2
2) PhRlh
2 2 1/2
(l+PhRlh)
h lh
G2 = AN 2 (2A*Dr
+ 3B-Dr
2)
PhR 2 h
(3-50 )
(3-51 )
22
1/2
(1+PhR )1/2
h 2h
2 hR3
G3 = AN 3 (2-ADr 3 + 3.B.Dr3 ) P h 3h
(3-52 )
(l+P R )/2
h 3h
2 1
G5 = AN 1 (A
3
2
BDr 1 ) Rlh J12
(i+phRlh)
22
+ AN
h lh
-
FADr2
+
2
B-Dr 3)
2
(l+P 2 R 2 ) 3 / 2 _
h
lh
R2
R2h
1
2 2
1/2
+PhR2h )
138
-
PR2h
(1+PhR
2
h)
h 2h
1
J
2
1
+ AN 3(ADr2+ B'Dr)] R3h [
-3
3
1/2
22
(+PhR3h)
P2 R
I_
2
_h 3h'
(+PhRh2
(3-53)
h 3h
)3/2
I
Therefore
dMth = G
dt
dDr1
dt
G dDr
+
2
dt
2dt
+ G3dDr3
dt
+ G 5 dPh
dt
(3-54 )
In Chapter 2 yarn torque at the cold zone entrance was derived
as
tc = Torquefiber tension
+
Torquefiber bending
+ Torquefiber torsion
( 3-55
2
BN
lc
BN1
Mtc = PcEcec
l(1+P2 Rc2
c
1/2
c
R2
2
2c
2
1/2
( l+P R2 C)
c3c 1/
'(l+p2R~c)
BN P3R2
1
+(EI) fiber
c
2 22
ic
3/2
1(1+Pc R Ic )
3 2
BN33*P c R 3c
+
(1+P 2 R2
c 3c
)3/2 I
139
+
3R2
2 c 2c
(l+PR22 3/2
)
fBN
(GIp)fiber
+
c 2c
+
BN 1 Pc
(1+P R 2 )3/2
I
+ BN2 Pc
(1+P 2 R 2
P
cI
BN 3
)3/2
c
( 3-56
)
2 R 23)/2
c 3c )
(p
Equation ( 3-56) is differentiated with respect to time to
obtain
dMtc
dt
P *E
dec
dt
BN1 Rlc
(1+P R2 )1/2
c
BN 2 R 2
+ 2
c
+BN3R2
2c
t
+ec
E (Plc
*[BN
i
2
c 3c)1/ J
2 4
PR
R2
lc
+
+ BN2
(1+P 2 R2
c2
2 2
c(+P
R c
1/2
22
cc
P2R 4
[R22c
2
]
c 2c
2
1/2
(1+P R 2
c 2c
]
)3/2
2 4
(1+P
cR2cc))1/2
(l+PcR
/
3
*IBN~
N11
L-
140
dP
c R3c
c lc
(l+P2R2
c c )3/2
c
dt
(1+P2R2c)
3/2
2 2
+ 3.(EI)
3-f(EI)iber
+
I
P4R4
c lc
(1+P2R2
c
5/2
.22
+BN 2
(1+P2R2
c 2
(1+p2 2
c 3/2
22
+BN3
P4
RJ
-.
Pc 2c
c 2c
5/2
44
PcR3
. dP.
. P.cR3c
c 3c
2
l+c R3c
c 3c
5/2J
dt
i'
I
+(GIp)fiber
[BN + BN1
,
'd c
3/2
c Ic
2 2
3P R
c
c
(1+P2R2
c )5/
c
+BN
222
3P2R
1
(1+P2R2 )3/2
c 2c
+BN 3
c 22
(1+P R
c 2c )5/2 I
1 2.,/
( 3-57
. (l+PR3c 3c )
)
c 3c
In order to simplify equation ( 3-57) we define the first
term of ( 3-57) which is multiplied by dec
as G6 and the
dP
remainder of the terms which are multiplied by dPc
dt
as
G 7 so that
dMtc =
dt
G
dec
6d-t
+ G
cdP
7 dt-
141
(3-58 )
Since tension at the cold zone entrance is equal to tension
at the hot zone entrance
Tensionold = Tensionhot
and torque at the cold zone entrance is equal to torque at
the hot zone entrance
Torquecold = Torqueho t
the time derivatives of these relations must also be equal
dTensioncold
dt
=
dTensionhot
dt
(3-59 )
=
dTorqueho t
dt
(3-60 )
dt
Now substituting ( 3-42 ), (3-47 ), (3-54 ), and (3-58 ) into
(3-59) and (3-60 ) we obtain
O=F 0
dDr
-O
dt
+ F
5
0 = G
dPh
dt
dDr1
+ F 1 dDrl + F
dt
F
dec
6 dt
- F7
dP
dt
-G
dPc
7dt
dt
142
dDR 3
dt
(3-61 )
c
dt
+ G 2 dDr2 + G dDr3 + G
dt
- G
dec
dt
dDr2 + F
dt
dt
dPh
dt
(3-62 )
Equations (3-61 ) and (3-62 ) are rearranged to obtain
dec
F.
dt
F6
+ F5
dPh
F6
r-0 + F1 dr
dt
-
dt
F6
F7
dPc
F6
dt
de
G 1 dDr
Wt
G6
dt
G7
dPc
G6
dt
-
dt
+ F
+
22
F6
dt
3
F6
dDr 3
dt
(3-63
+ G2
dDr
+ G3
G6
dt
G6
3
dt
+ G5
G6
)
h
dt
( 3-64 )
Equations ( 3-63) and ( 3-64) represent generalized threadline force coupled differential equations.
Seven dependent
variables (unknowns) are present in these two coupled equations.
To determine threadline torque and threadline tension
during transient operation it is necessary to consider in
addition, appropriate material balance and turn balance relations for each zone in the texturing threadline.
As stated
in the introduction to this section two models will be used
for determining local material balances and turn balances.
Both models will be applied to equations ( 3-63) and ( 3-64).
143
3.3.3.2
General Material and Turn Balances for the Hot
Zone and the Post Spindle 'Zone
Common to both analytical models of transient behavior
are the material balances and turn balances for the hot zone
and post spindle zone.
Along these zones the twist level is
observed to be essentially uniform for both steady state and
transient operation of the texturing system.
Material Balance for Hot Zone
In Chapter 2 it was pointed out that each radial layer of
filaments in the hot drawing zone has a unique draw ratio,
therefore it is necessary to formulate a separate material
balance for each layer, i.e.:
A(Materia)ho
Materialin
Materialou
t
t
The material balance for each radial layer can be quantitatively formulated as
AL
-
3i
h
V
sec i
sec
-r
3sec3i
Dri
144
( 3-65 )
where
Lh = Hot zone length
and as
At + 0
I
2hI
PhRih
(2+PR2
h ih
2 2
. (l+PiRih
'1'
1/2
dt
.
-i
(1+P2R2 )1/2
Lh
dDr.
dt
_
Dri i
1)/2
).
2 2
1/2
V3 .(l+PhRih).
-
dt
( 3-66
LhDri
Equation ( 3-66) can be rearranged:
2
V2
2 2
ih
Lhoph.R
7
,(l+phRi)
V (1+P2R
12
1/2
r
. -1
Tdt
Rr
2R2
fh
2
Dr
c ic
-1 ( +P2R?
2 2
(1+P Ric)
)1 /2
dPh
1
1/2
(+P hR ih)
2(+p2
1/2
c ic)
dDr i
dt
(3-67 )
Equation ( 3-67) represents independent equations depending
on how many radial layers of filaments exist in the hot zone.
This equation can be simplified by defining
2
P.R
Phih
L
ALh
Ail
-
(1+PhRih)/2
h ih
Ai2
i3
(1+P2R2 ) /
c ic
ih)
V3 (l+PR
Dr (+P 2 R? )l/2
1
A
,1
( 3-68)
ri
( 3-69)
c ic
22L+P1 / 2
- Lh (+Ph Rih
2-22
Dr. (l+
-- 1
1/2
R. )/2
C lC
145
(3-70)
)
Then,
V
A
V2
dP h
Ail dt
+
A
i2A
i3
d.r i
(3-71
dt
Turn Balance for Hot Zone
The quantitative basis for the turn balance is simply that
the rate of change of the number
of turns of twist in a given
yarn zone equals the difference in the angular velocities at
the ends of the zone, plus the net rate of transport of twist
to and from the zone.
Following this a turn balance for the
hot zone can be expressed as
A
(LhPh)
Wh-
Wc +
PcV2 PhV
3
(3-72 )
At + O
and as
dP
Wh
dt
-
W + PcV2 - PhV3
(3-73)
Lh
Material Balance in the Post Spindle Zone
During steady state operation, twist generally is not present in the post spindle region if the feed yarn is initially
twist free.
However, during transient operation twist does
occur in the post spindle region and this twist may affect
the linear speed of the yarn as it moves downstream through
the spindle.
ulated
The material balance in the zone can be form-
as
146
A
TE (LPsCrP ) =Vb
V
where
Crs
-PS=
Lps
s
4
( 3-74 )
4
Twist contraction factor in post spindle
= Post spindle zone length.
as At + 0 (3-74) becomes
L
P
Lps
2
2
R
(1+P2R2
-
dP .
ps 3h
Vb (l+(l+P2 R 2 )/2)
2
)1/2
s 3h
(1+(l+P2 R 2 )1/2)
ps 3h
4
i-
(3-75)
Turn Balance in the Post Spindle
The post spindle turn balance is formulated as
psps )
a (LP
~s
and as
= (VbP - V4P
4ps -W
(3-76)
s
)
At -+ 0
dP
Pts = VbPs
Lps
dt
-V
4 Pps
-
(3-77 )
W
s
Combine (3-75) and (3-77) to obtain
+W
V P
s
dP
dt
(1+(1+PR)
s 3h
=17*S
P
R
ps 3h
)
v4((1+PpsR
4
S3h )1
(l+(l+p2R2 )1/2)
s3h
P
R2
t(1+Pps 3h )/2
5
J
(3-78 )
147
Equation (3-78 ) can be substituted into ( 3-77) to obtain
4Ps
V
s
where
'
+Lp
P
P
(3-79)
dt
Vb = The linear velocity of twisted yarn as it
enters the spindle.
3.3.3.3
Material and Turn Balances for the'Cold and
Cooling Zones: Model 1 - Flat Twist Distribution
Material Balance in Cold zone
In Chapter 2 it was assumed that all of the filaments in the
twisted yarn of the cold zone are under equal tension and
therefore equal axial strain.
With this consideration it is
only necessary to have one material balance equation that
represents all cold filaments.
The material balance in the
cold zone is quantitatively expressed as
A
'C = V-
C
V2-c
l+e c
as
At
A
1
l+ec
( 3-80)
l+ec
0
dCrc
Cr.
-- c
dt
2
dec
c
dt
V
Lc
c
(l+ec)
V2
L
c
(
Cr.
- c
(l+e)
c
3-81
where
Cr
= 1/2
(l+PcR
/2
l
)
(PR
PcR 3 c
... ... (
. 3-82 )
* Note: Cold twist contraction factor obtained by radial
averaging method.
148
2
PcR3
c 3c
ZZE
1
2(PPcR3c
1/2)
c c 3c + (1+PcR2c
~c3c'
2(1+PcRc)1/2
c 3c
+
2 (1+P2 R
c
c
)1/2 (P
in
(PcR3 +(1+P2R
2P2 R
(1+P
R
+(1+PR
2
3
)
1/2
)1/2
( 3-83
)
( 3-84
)
(3-85
)
3c
and
dCr
dt
= Z dPC
dt
Substitution of ( 3-84) into ( 3-81) gives
2
l+e
= Cr
r
V0
-c
ZL
c
Cr
dP
-c
c
de
+ Lc
dt
1+e
c
c
dt
Equation (3-85) can be simplified by defining
Q
Q1-
L
(3-86 )
C
c
c
Q2
l+e
c·
V0
Cr
-c
Q
3-
(3-87)
ZLc
Cr
(3-88 )
c
Then
V2 = Q 1
c
dt
+ Q2
Q3
149
c
dt
(3-89 )
Equations ( 3-71 ) and ( 3-89) can be coupled to obtain
dDr
dt
Ail
Ai3
Ph
dt
+
Ai2
Ai3
Q1 dec
Ai3 dt
Q2 + Q 3
dPc
Ai3 dt
Ai3
(3-90)
Equation (3-90) represents as many equations as there are
radial layers of filaments plus the central layer at the hot
zone entrance.
As stated earlier, most yarns which are pres-
ently being draw textured consist of one core filament and
three radial layers.
Accordingly, from this point on it will
be assumed that the yarns have but one core and three layers.
If larger yarns are encountered appropriate arithemetical
changes can be made, still, the threadline physics would
remain unchanged. Equation ( 3-90) is substituted into (3-63)
to obtain
dec
dt
F
F6
Q3
A01
A03
dPh
dt
+ A02
Q1.
-
dec
A 0 3 dt
A 03
dP
A 03 dt
+ F1
All
dPh + A 1 2 - Q2
Q1
F6
A13
dt
A 13 dt
A13
150
dec + Q3
dP
A 1 3 dt
+F 2
A 21
dP h
F6
A23
dt
+
+ F 5. dP h
F6
+ A 3 2 - Q2
h
dt
A 33
F6
A23
A 23
+ F3 , A31 ,
dt
6
Q
dPc
3
A23 dt
dt
- Q1 dec + Q3
dPc
A 3 3 dt
A 33 dt
A33
- F7
+
Q. dec
-
A22 - Q2
dP
.
C
dt
( 3-91
)
Equation ( 3-91) can be simplified by introducing abbreviated
symbols
X
=
1
0.
F6
01
+ F1
A11
+ F2
A21
a03
F6
A13
F6
A23
+
3
F6
31
A3 3
5
F6
( 3-92
X
FO
Q1
x2=6
03
F6
+
A03
F1
F6
+ F2
Q1
A13
Q1 + F 3
F6
A23
F6
Q1
A33
( 3-93
X
- FOQ3
+
+
F 1Q 3
F2Q3
F6A13
F6A03
+
F6A 23
)
)
F3 Q 3
- F7
F6 A33
F6
6 03
( 3-94)
XA
_I = F 0
(A02 -
F6
A03
+
F1
F6A13
+ F 3 (A32 - Q 2 )
F 6 A3 3
(A1 2
- Q2)F 2(A22 Q2)
F 6A 23
( 3-95)
151
Equations (3-92 ), (3-93 ), ( 3-94), ( 3-95) are substituted
into (3-91 ) to obtain
dec = X 1 dPh
dt
1'X2 dt
+
X 3 dP C
1-X2 dt
+
X4
1-X2
(3-96
)
(3-97
)
( 3-98
)
( 399
)
Likewise the following symbols can be defined
G
A
+ G2A21 +
Y 1 A11
G6
Y-2
G1
G6
+
A Q1
A13
G6
A1 3
G1
G6A13
G6
+
G 2Q 1
G2
G6
G6 A 33
Q 3 + G 3Q 3
A 23
G 6A 33
(A1 2 - Q2)
+
G7
G5
(A2 2 - Q2 )
G2
G6 23
6 13
+ G3
G6
A33
G 3Q 1
G6 23
+
G3
1
Y
G6 A 23
A13
+ G5
G3, A31
*(A3 2 - Q2 )
G6A33
( 3-100)
6 33
Finally we substitute ( 3-97), ( 3-98), ( 3-99), (3-100) into
( 3-62) to obtain
de
dt
=
Y1
1-Y2
dPh
dt
+
Y3
1-Y 2
dPc
dt
+
Y4
1-Y2
( 3-101 )
Equation (3-101) and Equation (3-100) represent two simultaneous first order differential equations with three unknown
time derivatives and seven unknown variables.
152
Turn Balance in the Cold Zone
In Chapter 2 it was shown that during steady state operation
of the draw texturing process the cold zone twist level is a
fraction of the hot zone twist level.
Since we assume that
the hot zone rotates at the same angular velocity of the pin
spindle, the angular velocity of the cold zone must be somewhat less.
The turn balance for the cold zone can be quantified as
A
(LcPc)=
(3-102)
At + 0
and as
dP
c
dt
where
Wc -PcV2
W
c
W -P V
c c2
L
=
( 3-103)
c
= The unknown rotational velocity of the cold zone
The cold zone turn balance (3-104) can be added to the hot
zone
turn balance( 3-73) to obtain
L
W
Whh
h
dt
L= dPc
dt
- PhV
(3-104)
To simplify equations (3-104) the following symbols are
defined as
X
5
Wh -PhV
L
3
Lh
X
L
c
dP
3-105 )
c
~~~~~Lh
153
~( dt
3-106)
so that
-104 ) becomes
dPh = X - X dPh
dt
5
6 dt
(3-107)
Material Balance in the Cooling Zone
During steady state operation, the linear speed of the twisted yarn as it leaves
the hot zone is assumed
equal to the
linear speed of the yarn as it approaches the rotating pin
spindle, i.e., there is no material buildup in the cooling
zone.
During transient operation this is not the case and
a material balance over the zone is necessary.
A
where
(LsCrset
VCrV
-
V-hot
br et(3-108)
(3-108)
Crset = Twist contraction factor all along the cooling zone
and as
At + 0
L
Ls
2
-Vb
PR
s 3h
(l+P2R2h) 1/2
s 3h
(+(l+P 2 R 2
2
s 3h
dP
=
dt
1/2
v
V3
2
2 2 1/2
(l+(l+P 2 R
)
(3-109)
For Model 1 the assumption is made that the twist in the set
zone is equal to the twist in the hot zone at all times.
Therefore
Ps
Ph
(3-110)
154
Then (3-109) becomes
2
LP hR3h
V=
h22
1 dPh
dt
2 2
1/2
(lPhR3h
+ Vb
+PR3h
h
(3-111)
Equation (3-111) is now substituted into (3-69 ) so that
A2
L P R
s hR3h
=
dP
dPh
+ 1+PhR3h
(1+P2R2)1/2
h 3hh 3h
+ Vb
dt
2 2
1/2
(l+p2R2
)1/2
Dr
-1 (l+P2R2
c ic )1/2
( 3-112
Ai2 is now substituted into (3-90).
defined
)
Ail and Ai2 are re-
as
LPR
A _LhPhRih
2
Ai
-
i
=
h ih )1/2 (+P2R2
c ic ) 1/2Dr.
-
(1+P R
2
L P
(1+PhRih )/2
s h 3h
+1
2 2
(l+Ph 3h>
1 2
2
2R
2v1+
A.
= V b +( l P
+ 1 +
2 2
h 3h
Dr (l+p2 R2
-
1 /2
C iC
( 3-113
)
( 3-114
)
1 /2
h R lh
Dr1i (l+p2R
C 1C )1/2
Turn Balance in the Cooling Zone
A turn balance is formulated for the cooling zone.
A
(LsPs)
= V3Ph -Vb
155
s
(3-115)
where
Ls
and with
Ph = Ps (assumed for model 1)
Length of cooling zone
s
We also assume that there is no difference in the net rates
of rotation at the ends of the zone.
dP
L
s dph
dt~
S
Adding
= VP
3
h
V
(3-116 )
- VbP
bh
(3-116) to (3-107) the following
turn balance
is
derived for the full texturing zone.
(Lh + Ls ) dPh
dt
=
dP
Whh- Lc-dc
- PhVb
hb
(3-117 )
Defining
X 5 - Wh-PhVb
(Lh+Ls)
6
L
=
(3-118 )
c
(3-119 )
Lh+Ls
To get
dPh
dt
Equation
=
X
dP
- X
5
(3-120 )
c
dt
6
(3-120) is now substituted into Equations (3-96 ),
and ( 3-101) to obtain
dec = Y 1X 5 +Y4
dt
de c = XlX5+X4
dt
+
Y3-Y1X6
1-Y2
dPc
dt
( 3-121)
+
X3-X 1X 6
l-X2
dPc
dt
(3-122 )
1-Y 2
1-X2
156
Equations ( 3-121) and (3-122)are coupled to obtain
_
YlX5+Y4
XlX5+X4
1-X 2
( 3-123
)
( 3-124
)
1-Y
Equation (-123 ) can be functionally expressed as
dP
dt
c = Z 1(P ce Ph
c
c-
Dr., Pps )
P
Equation (3-123 ) is substituted into (3-120 ) to obtain
dPh = Z2 (Pc
dt
2
c
Ph
h
e c,Dr,
)
ps
-
Ps
Equation (3-125) is then substituted
de
into
c = Z3 (Pc Ph ec',Dr.iP
)
ps
c-
(3-124),
(3-125) and
)
(3-121) to obtain
( 3-126
dt
Equations
( 3-125
)
(3-126) are now substituted
into (3-90 ) to obtain
dt
dt
=
(3-127 )
Z4(PcPhecDriPPps)
Finally
dt
dPs = Z (PcPh,e
5
,Dr
i
c-
P
)
ps
(3-128 )
Threadline tension is obtained by solving the preceeding set
of five differential equations and substituting values of ec,
157
P
c
into (3-43 ).
Finally, these values of e,
and P are
c
also substituted into (3-56 ) to obtain threadline torque.
3.3.3.4
Twist Transport, Material Balances and Turn
Balances in the Cold and Cooling Zones: Model 2
- Tilted Twist Distribution
Twist Transport Formula of the Tilted Twist Model 2
The previous model (MODEL 1) for transient operation was
based on the physical simplification that uniform twist levels
during transient operation persist in each of the four zones
of the threadline (cold, hot, cooling, and post spindle).
Actual photographic measurements of twist as a function of
time and position after a step change in spindle speed, indicate that the twist level in both the cold and cooling zones
is not uniform with position during transient operation.
Experimental evidence presented earlier, in Section 3.2.3,
indicates that twist changes incurred at the entrance to the
cold or cooling zones propagate downstream with the movement
of the threadline.
As a first approximation the twist level
in either the cold zone or the cooling zone can be considered
to vary linearly with position along that zone.
ution is illustrated on the following page.
158
This distrib-
I
I
VAt
H
pJ
P1
I
L--J--I
.-0
2 -
bk
r
'
·
ZONE LENGTH
This model of the twist distribution operates as follows.
At position C, (which is the downstream limit of the zone in
question) the twist level at anytime,t, is P1 .
At the same
time,t, the twist level at position A,(the upstream end of
the zone), is P2.
P 2 is dictated by threadline mechanics.
At position B, located a distance VAt upstream of C, the
twist for time, t, is P1 + AP1 .
During the time interval At
the twist at position B migrates downstream to position C
establishing the new twist level there as P1 + AP1 .
It fol-
lows that:
( 3-129)
P2P1 = P1
L
VAt
159
where V is the linear yarn velocity at C.
Now, letting
At + 0
dPl
dt
P1)
(P2L
V
(3-130 )
This twist transport relation is now inserted in subsequent
treatments of material and turn balances for the cold and
cooling zones.
Material Balance in the Cold Zone for the Tilted Twist Model 2
We have assumed that the twist distribution in the cold zone
varies linearly along the threadline during transient operation.
Therefore the length of material in the cold zone is
Crc + Cr
+e c
L
2
Further, we assume that the constant filament strain which
obtains at the entrance to the cold zone at a given time,t,
is uniform along the cold zone.
Since filament strains at the
cold zone entrance are of the order of 1% or less, the error
introduced by this assumption in the following expressions is
seen to be negligible.
The material balance in the cold zone
is
ALc
At
where
Cr
[Cr
+ Cr.
2 l1+e
I
-
2Cr-
(l+ec)
(3-131)
= Cold twist contraction factor at downstream
end of the cold zone
160
as
At + O
V
dCr
c
*
-c
2Cr
dt
_j
Cr.
-]
+ Lc
Cr
let
dt
where
1
=
dt
2
PR
c 3c
q%
(l+PcR3
c 3c
and
dCr.
1
)/
-I
dt
(-3-132 )
( 3-133)
+
-;
2Cr.
dt
J
dP
dCr.
c
.de
Cr. (1+e)
= Z
dCr
+ Cr.
-
2
L
L
= (l+ec)V 0
1
I
(PcR3c+ (1+PR3 c)1/2) (3-134 )
dP.
3
= Z2
dt
(3-135 )
dt
R2
where
P .R
Z22 =
1
+
3c
1
(P(P
(1+PjR3c)/2
3c
R
+(1+P 2R 2 )1/2)
(P (P3c
j 3c
( 3-136)
where
c
Pj = Cold twist per twisted length at cold zone exit.
Then equation (3-132) can be expressed as
V
2
- L
= (l+ec)
Cr.
o
,Zc
2Cr
-J
]
L
Cr
2
Crj l+ec)
dP
dPc
z ldt
°
-
L
c
2Cr.
-J
Z2
dP.
3
dt
+ Cr.
+ c.rc
-+ede
d{
(3-137 )
The twist transport relation for the cold zone is
dP
dt
dt
P
c
-
L
P.
j .V2
(3-138 )
c
161
Equation (3-138)
V2
-
is now substituted into (3-137) to obtain
1+ (Pc
P.)Z2
2Cr.
=
J
+ 'c. SE+
C
2
l +e
Cr
-J
V
- Lc
2Cr
Z
dP
dt
-dj
d(3-139)
ude
Cr.j(l+e )
-J
dt
C
Equation (3-139 ) can be simplified by defining
L
Q 1
c
Cr
+ Cr. |
-
1+(Pc
( 3-140
)
( 3-141
)
Pj)Z2
2Crj
(l+ec)
21 +(Pc - P
)Z
2Cr.
,,-]
Q33--
LcZ1
I1+
(Pc-Pj)
2 (2Cr
2Cr.
3
(3-142 )
-3
Equations (3-140), (3-141), and (3-142) are now substituted
into (3-89
) in place of ( 3-86),
(3-87), and ( 3-88), so
that V2 is still expressed as
V2 = Q1 de
dt
+
Q2 - Q3 dP c
2
162
( 3-89 )
Material Balance in the Cooling Zone for the Tilted Twist
Model
2.
If we assume that the twist distribution in the cooling zone
is linear as seen in thetwist sketchthe length of the cooling
zone segment in its untwisted
L
state is
s (Crh + Cr )
2
The mass balance in the cooling zone is then
(h
L
Ats
~~t
where
+
Cs) = V
2
Crh - V Cr
( 3-143 )
b-s
3 -
Cr
-h = Twist contraction factor at upstream end of
set zone
= Twist contraction factor at downstream end of
Cr
set zone.
Using Hearle's expression for twist contraction we convert
( 3-143 ) to
L
S 2
PhR32
h
R3h
2 2
2
0
dP
1/2 dt
h 3h
V3
2
h
(1+ (l+P2R2 )1/
h 3h
+
PR
3h
s(3h
2
*
2
2(l1+P R2)
1/2
dP s
dt
s 3h
- Vb (l+(l+P2 R2 )1/2
2
s 3h
( 3-144 )
The twist transport equation for the cooling zone
163
dPs = (Ph-Ps)
dt
L
is substituted
(3-145 )
s
in (3-144) to obtain
=
3
Vb
s
L
P
2
.
PhR3h
12 PR
.dP
2 2
1/2
2
22+pRh
hlP;3h
(11+(l+PhR~h)
h3
Ph
dt
) Vb
2
PR
3h(P-P)V
s 3h
h sb
+
2 (1+Ps2 R2
)1/2
3h
(1+(1+P2h R3h)/2
)
3h
(1+(1+P2 R2 )1/2)
+ Vb (1
s(1
R3h)
(1+(l+P2 R2 )1/2)
h3h
(3-146
)
Equation (3-146) is now substituted into (3-69 ) with Ail,
Ai2, Ai3'
defined
Aii
as
L
PR 2
LhPhRih
2 2 )1/2 (1+PhR
2
)) Dr.
Dr
(1+P.R.
1/2 LsPhR3h (+P2R2h)
+
(1+P2
2
2 1/
(l+PhR3h)
(1+(+P
2
2
R
)1/2
+PhR3h)
164
/
22
1/22 Dr(+PR
Dr
(1+P(R
h 3h h 3h (3-147ic
(3-147 )
A2
(lA (1+P2.R2h)1/
s 3h
2
R2h) 1/2
(1+ +2
1
). (l+P2
Dr
/2)
ih
sR23h (Ph-Ps)(1+PhR,2
2 (l+P2Rh
/2
)/2
(+PR
1/2
(l+(l+PhR
3 h) )
Dr
(1+PR
2
( 3-148
i3
which
Lh (1+P2R2h)1 /2
Dr? (l+PR 2 c)1/2
)
( 3-149 )
leads to :
V 2 = A il
dP
h
dDr.
+ Ai 2 - Ai3 d
( 3-150)
dt
dt
Equation (3-150) can be added to ( 3-89) and an expression
is obtained for the time derivative of the draw ratio for
each filament layer in the yarn.
This expression is identical
to equation ( 3-90) for the time derivative of draw ratio for
the flat twist distribution Model #1.
sions for Ail' Ai2' Ai3' Q1 ' Q 2' and
ferently,
i.e., as shown
in (3-147),
However, the expres3 are now defined dif(3-148),
(3-149),
(3-140), (3-141) and (3-142) for the case of the tilted twist
Model
#2.
Turn Balances
A turn balance exists for each of the four zones (cold, hot,
165
cooling, and post spindle).
Each turn balance requires that
in a given zone, the rate of change of the number of turns in
a given zone is equal to the difference in the rates of rotation of the yarns at the ends of the zone plus the net gain by
transport to and from the adjacent zones.
As in Model 1 we
assume here that the twist levels are uniform along the hot
and post spindle zones.
Turn Balance in the Cold Zone for the Tilted Twist Model 2
We assume that if the twist varies linearly in the cold zone
from Pc to Pj, then the amount of turns in the cold zone is
L
A
(P +P.)
c j
2
Therefore the cold zone twist balance is
A [Lc(Pc+Pc) 1
At
where
W
- PjV
c
2
2
(3-151)
(3-151)
P. = Cold twist per twisted length at downstream
end of the cold zone
and as
At + O
L
2
c.dP. + L c.dP c =W- PV 2
dt
2
dt
c
(3-152)
Turn Balance in the Hot Zone
The hot zone turn balance for Model 2 is the same as for
Model
1, i.e.:
166
Lh dP h= h Wh
W + p
(3-153 )
2
Turn Balance in the Cooling Zone for the Tilted Twi'st'
Model 2
If we assume that the twist distribution is linear in the cooling zone, the number of turns in that zone is
L
Ph+Ps
sT
s
The cooling zone twist balance in then:
A
Ls (Ph+Ps) =PhV3
sE
and as
- PsVb + Ws
Wh
2
( 3-154
)
( 3-155
)
0
At
Ls
dPh + Ls
dPs
2
dt-
dt
2
= PhV3 - PsVb + Ws - Wh
Observation indicates that for practical purposes Wh = W s
where
Wh = Angular speed of hot zone segments
W
= Angular speed of cooling zone segments
A composite turn balance for all zones upstream of the spindle
is formulated by adding the cold, hot, and cooling zone turn
balances to obtain
Lc dPc + Lc
dPi
2
dt
dt
2
+
' dPh
dt
= Ws - PsVb
+ L
2
dPh +s Ls dPs
dt
2
dt
( 3-156 )
167
The twist transport equation for
dP
dP
j and
s can be substitdt
dt
uted in (3-156) to obtain.
1/2
+
{(P-Pj)V2
+{Lh dPh 1
I dPc--+ 1/2
c
2
hdpI
~~~~~~d
d-J
/2 L
dth + 1/2
{(Ph Ps)lVb
dt~~~~~~
= Wh
PsVb
Vb is determined by the post spindle analysis.
(3-157 )
V 2 is obtained
from the cold material balance.
V
= Q
de + Q
dt
dP
- Q 3 c
dt
(3-158 )
Substituting V 2 into the composite turn balance we obtain
dPh =
dt
Wh-PsVb
Lh+l/2 Ls
- 1/2 (Ph-Ps)Vb
Lhh + L ss
-
+ 1/2(P -P)Q3
Q (P -Pj)
2 Lh
de
+ Ls I dt
-
dP
c
Lh+l/2
Lh+1/2 L s
-
L
Ls
c
dt
Q (Pc-Pj)
2 2L+L
2Lh+Ls
(3-159)
We now define
X - WhPsVb
5
X
Lh+l/2 L s
-
( 3-160
)
( 3-161
)
L
c
2Lh + L s
h
168
-
X7
X
.
c
-P .'
2 Lh+
(3-162 )
Ls
(Ph-Ps)Vb
2 Lh+
Ls
(3-163 )
so that
dPh = X 5 + (Q3 X 7 - X6 ) dPc -
dt3
dt
Q1X7 de - Q2 X7 - x 8
1
adt
(3-164 )
Using the values of Ail,Ai2,Ai 3 ,Q1 ,Q 2 ,and Q3 for Model 2 a
new set of X'X2'X3'X4,Y1,Y2Y3,
and Y4 can be obtained from
equations (3-92 ), (3-93 ), (3-94 ), (3-95 ),
( 3-97 ), ( 3-98 ), ( 3-99 ) and ( 3-100)- The general
threadline force equations are then expressed as:
(1-X2) de
dt
= X1 dh
dt
+ X3
c
dt
+ X4
( 3-165)
and
(1-Y2 ) de = Y1 dPh
dt
dt
+ Y3
dPc
dt
+ Y4
( 3-166)
substituting the composite turn balance ( 3-164) into ( 3-165)
and ( 3-166 ) we obtain
(1-X2 ) de = X 1
dt
Q
8
2X 7-X
X5
+ (Q3 X 7 - X6 ) dPc - Q1 X 7 de
dt
dt
+X dPc
dt+ X
169
(3-167
)
and
(1-Y 2 ) de = Y 1 X 5 +(Q3 X 7 - X 6 ) dPc - Q1 X7 de
dt
dt
dt
Q 2 X7
X
8
+ Y3 dt
(3-168 )
Equations (3-167 ) and (3-168 ) are combined to obtain
X 1 X 5 -Xl
1 Q 2 X7-XlX8 +X4
Y1X5-Y 1Q 2 X 7-X 1X8 +Y 4
dPc =
dt
1-Y2+Y1Q1X7
X1Q3 X7 - X1 X6 +X3
L 1-X2 + XlQlX7
1-X 2+XlQlX
7
-
Y 1 Q 3 X 7 - Y1 X6 + Y3
1-Y2 + Y1 QlX 7
( 3-169)
Equation ( 3-169) can be functionally expressed as
dP
Dr.)
dtdc = Y 1(Pc'PjPh'Ps'Pps'ec'DP
c
h" s ps ec-i
( 3-170)
Equation ( 3-170) is then substituted into ( 3-168) to obtain
de = Y3 (Pc'Pj'h'Ps'Ppsec'
( 3-171)
Dri)
Equations ( 3-170) and ( 3-171) are substituted into the composite turn balance to obtain
dPh
h
)
d = Y2(Pc'PjPh'Ps'Pps'ec'Dri
)
dt
Equations ( 3-170),
( 3-171) and (3-172)
into ( 3-90 ) to obtain
170
( 3-172 )
are substituted
dDr·
3-90 )
- = Y4(PcPhPj
,
PsPps ,Drie
c)
dt
Finally
dPt
(3-173 )
Y5(Pc'Ph'Pj Ps'Pps',Dri'ec)
dP
dt s
dP
(3-174)
Y6(Pc'Ph'PjPs'Pps'Driec)
dt
Y7 (Pc 'Pj Ph'PsPps
Dri'ec)
(3-175)
Threadline tension and torque are obtained by solving the preceeding set of differential equations and substituting values
of ec,Pc , into equations ( 3-43) and ( 3-56).
3.3.4
Solution Technique for the Transient Analysis
Each of the analytical models of transient threadline
mechanics is represented by a system of non-linear ordinary
differential equations.
The transient solution to these sys-
tems of equations is solved by the DYSYS(DYnamic SYstem
Simulation) subroutine provided in the MIT Mechanical and
Civil Engineering Joint Computer Facility.
DYSYS uses a
fourth order Runge-Kutta integration to obtain approximate
solutions to the system of equations. The form of equations
which DYSYS can solve is:
d
dt
Y 1 = fl(t, Y 1
.... )yn
171
d
Y 2 = f 2 (tYl'Y
2
.........
dt
d
dt
Yn = fn(tYlY2
......
This may be compactly written as:
d
Y = F(t,y)
dt
where Y is an n-dimensional vector made up of the current values of Yl ....Yn and F is a vector valued
of the current values
of f
function
composed
.... f
The Computer programs that use DYSYS to give transient solutions are listed in Appendix
6
for Model 1 and 2.
The
initial values for the transient analysis are obtained from
solutions derived from the steady state analysis presented in
Chapter
2.
172
3.4
EXPERIMENTAL STUDY OF TRANSIENT OPERATION OF THE DRAW
TEXTURING PROCESS: USING POY POLYESTER
Experiments were done with POY polyester yarns supplied
by the Du Pont Company so that we could compare measured
threadline behavior,
.e. threadline tension, torque, and
twist distribution, with predicted results during transient
operation of the draw texturing process.
The dimensions and
properties of these yarns are given in Section 2.4.1.
yarns are textured on the MITEX False Twister.
The
Threadline
torque and tension were measured by the MITEX Torque-Tension
Meter placed slightly downstream of the feed rollers.
The
placement of the latter device at this position causes the
actual length of the threadline to be increased by the distance from the feed rollers to the twist trap on the device,
but this added length has only a minimal effect on transient
threadline response since no twist is included in this extra
length.
For it is change in twist with respect to time which
affects threadline response most.
Finally, threadline twist
was measured optically by taking pictures of the threadline
at different stations along its length and counting twists.
Unsteady machine operation was activated by changing the
machine twist stepwise.
Three combinations of machine
dimensions were used in these experiments.
173
COLD ZONE HOT ZONE COOLING ZONE POST SPINDLE ZONE
Mode I
6.00"
1.25"
7.00"
9.00"
Mode II
6.00"
3.00"
5.25"
9.00"
Mode III 13.00"
1.25"
0.0 "
9.00"
The nominal yarn throughput speed was 0.47 inches per second;
the machine draw ratio was 1.60; the heater temperature was
2100 C.
Two complimentary sets of experiments were carried out
for each mode of machine operation.
In one set the process
was allowed to operate at steady state with the machine twist
at 50 TPI before the machine twist was step changed to 60 TPI.
For the complimentary set of experiments the machine twist
was reduced stepwise from 60 TPI to 50 TPI.
Table 3.4
lists the critical threadline responses during transient
operation for all experiments using POY polyester.
Twist Increased to 60 TPI from 50 TPI
Figures 3.29 , 3.30, and 3.31 show predicted and measured
transient tensions for each machine mode of operation.
The
predicted tensions using Analytical Model 2(tilted twist
distribution) compare favorably with the measured values
for Machine Mode I and Machine Mode II.
However, for Machine
Mode III the predicted results using Analytical Model I
(flat twist distribution) compares more favorably to the
measured results than the predictions using Model 2.
174
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should be emphasized that Mode III machine operation
does
not truly represent common texturing conditions since there
is no cooling zone in the threadline before the spindle.
Figures 3.32, 3.33, and 3.34 show predicted and measured
threadline torque for each mode of operation.
The predicted
torques using Analytical Model 2(tilted twist distribution)
compare favorably with the measured values for each mode of
machine operation.
It should be noted that when the cool-
ing zone length is shortened and the heater length increased
(Mode II) the peak torque is higher than for Mode I.
This
is due to the maximum tension in the threadline occuring at
a later time for Mode II than for Mode I; at a later time
the twist is higher and threadline torque is governed by
hot twist and threadline tension.
Twist Decreased to 50 TPI from 60 TPI
Figures 3.35, 3.36, and 3.37 show predicted and measured
threadline tension for each mode of machine operation.
The
predicted values using Analytical Model 2(tilted twist
distribution) compare favorably for the most part with the
measured values of threadline tension for all modes of
machine operation.
However, after the tension bottoms out
the predicted and measured values for Mode III are not
in good agreement.
Figures 3.38, 3.39, and 3.40 show predicted and measured
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threadline torque for each mode of machine operation.
The
predicted values using Analytical Model 2(tilted twist
distribution) compare favorably with the measured values
of threadline torque for all modes of machine operation.
Twist Distribution in the Cold Zone
Figures 3.41 and 3.42 show predicted and measured results
using Analytical Model 2(tilted twist distribution) for
threadline twist as functions of time at two positions
in the cold zone for Mode I machine operation.
Note the
steady state error between predicted and measured twist
values at 60 TPI machine twist.
twist the error is negligible.
However at 50 TPI machine
In light of steady state
errors, the measured and predicted transient threadline
twist levels compare favorably with each other.
In Figure
3.43 we connect the measured twist levels at two points in
the cold zone by a straight line at different times after
a step change in machine twist and compare the slopes of
these lines with the predicted slopes using Analytical
Model 2.
Comparison of the measured and predicted twist
distribution slopes at the same time indicates good agreement.
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3.5
EXPERIMENTS ON THE DRAW TEXTURING OF POY NYLON
Experiments were conducted on Du Pont POY nylon yarns
for the purpose of comparing measured values of threadline
parameters , i.e. threadline tension and threadline torque,
with predicted results during transient operation of the
draw texturing process.
The dimensions and properties of
the feed yarn used are as follows:
Undrawn Filament Radius:
90/34 - 2.65
-4
inches
3.57 x 10
Undrawn Filament Tensile
:
Modulus
268,000 psi
Undrawn Filament Denier:
Undrawn Filament Bending
Rigidity
:
-9
-
Undrawn Filament Torsional
Rigidity
:
2
lb in
3.42 x 10
2.47 x 10
2
lb in
Filament dimensions and tensile modulus were measured
in the Fibers and Polymers Laboratories at MIT.
The bending
modulus was calculated from the tensile modulus based on the
assumption of equal axial and compressive moduli.
The
torsional rigidity (GIp) was obtained from Ward(ll).
The yarns were textured on the MITEX False Twister.
Threadline tension and torque were measured by the MITEX
Torque-Tension Meter.
follows:
The machine dimensions were set as
Cold Zone
6.00 inches
Hot Zone
1.25 inches
Cooling Zone
7.00 inches
193
Post Spindle Zone:
9.00 inches
The unsteady machine operation was activated by introducing a step change in the machine twist.
The nominal
yarn throughput speed was .38 inches per second; the draw
ratio was 1.29; the heater temperature was 2100 C.
Steady State Threadline Tension and Threadline Torque
For this commercial textured
nylon yarn the general
level of machine twist is between 60 TPI and 70 TPI, and
so threadline tension and threadline torque were measured
and predicted
for these levels as indicated below:
Machine Twist
Tension, grams
Predicted Measured
Torque(10- 4 ) in lbs
Predicted Measured
60 TPI
23.3
26.5
.78
.86
70 TPI
20.9
23.0
.89
1.01
It is seen that the predicted values of threadline torque
and tension are about 10% less than the measured values.
No effort has been made to experimentally characterize in
full threadline behavior with this POY nylon.
The above
data were obtained to reinforce our confidence in the utility
of the steady state analysis of texturing threadline behavior,
which up to now was directed towards the POY PET yarn -machine
system.
It should be emphasized that the POY nylon feed yarn
differs significantly in dimensions and properties from the
194
POY PET yarns generally used in this study.
In particular
the nylon differs considerably in its rigidity ratio,
i.e. EI/GIp (1.38 for nylon versus 3.05 for PET), a quantity which can have considerable influence on the determination of cold zone twist and -torque.
Transient Threadline Tension and Torque
Using POY nylon described above, we also undertook
limited study of transient behavior during the draw texturing
process on the MITEX False Twister.
Threadline torque
and threadline tension were measured by the MITEX TorqueTension Meter.
Unsteady machine operation was activated
by changing the machine twist stepwise.
The texturing
machine dimensions were the same as those used for the steady
state study described above.
Figures 3.44 and 3.45 compare predicted threadline tension
and torque using Analytical Model 2(tilted twist distribution)
with measured values when the machine twist was changed from
60 TPI to 70 TPI.
It is noted that the time response for
tensions and torque maxima and minima are consistent for
experimental and calculated values.
There appears to be
considerable difference in transient tension and torque levels
but if we correct for the before and after steady state
error between the predicted and measured threadline tension
and torque, we conclude that the transient changes in thread-
195
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line tension and torque compares favorably with the measured
changes.
Likewise, Figures 3.46 and 3.47
compare the pre-
dicted threadline tension and torque using Analytical Model
2(tilted twist distribution) with the measured values when
the machine twist is dropped from 70 TPI to 60 TPI.
Again,
with the suggested steady state correction, predicted and
measured changes in threadline tension and torque compare
favorably, although one cannot claim the extent of agreements observed in the POY PET experimental study.
One point should be noted for the nylon yarn, i.e.
that the measured torque levels during transient operation
approach their new steady state levels virtually without
overshoot.
This behavior may play a role in preventing
the cycling of tension and torque during unsteady operation
as discussed
in Chapter
4.
198
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3.6
PREDICTED EFFECT OF OSCILLATORY OPERATION ON THREADLINE
RESPONSE
A commercial texturing machine running twenty four
hours a day is subject to all kinds of wear.
Critical
machine parts subjected to wear, such as feed rollers, take
up rollers, and spindle drive, may run unsteadily
changes in critical dimensions with use.
due to
This section
considers how machine tolerances affect threadline response.
The effect of three such operating defects will be examined
including:
3.6.1
1.
Oscillating Spindle Speed
2.
Oscillating Feed Roller Surface Speed
3.
Oscillating Take Up Roller Surface Speed
Oscillating Spindle Speed
Under normal texturing conditions the spindle speed is
assumed to be constant although wear in the spindle drive could
cause-the spindle speed to oscillate slightly above and below
the nominal speed.
To provide some understanding of how
oscillatory changes affect the threadline forces, we execute
the transient analysis given in Section 3.3 and program the
spindle speed to oscillate sinusoidally 1% above and below
the nominal spindle speed of 177.33 radians per second(60 TPI
Machine Twist).
The machine draw ratio was programmed as
1.60; the throughput speed was programmed as 0.47 inches
per second.
The frequencies of spindle speed disturbances
and corresponding peak to peak variation ratios are.:
201
FREQUENCY OF
PEAK TO PEAK VARIATION RATIO
SPINDLE
FORCED DISTURBANCE
THREADLINE THREADLINE
SPEED.
TENSION
TORQUE
.177 Radians/sec
.02
.0304
.0285
1.77 Radians/sec
.02
.0032
.0030
177. Radians/sec
.02
.0003
.0004
The predicted peak to peak variation ratios given
above show that as the frequency of the spindle speed disturbance increases, the effect on threadline behavior
decreases.
Accordingly, since the nominal speed is 177.
radians per second we can conclude that spindle speed disturbances near that frequency do not cause significant
variations in threadline behavior.
However if the disturbance
frequency is several orders of magnitude smaller than the
nominal spindle speed, the effect on threadline behavior is
more pronounced.
This finding is significant since one way of driving the
spindle is to use a magnetic roller (in contact with the
spindle) with a radius several orders larger than that of
the spindle radius.
If such a magnetic roller were to be-
come eccentric due to wear,the disturbing frequency would be
low enough to create substantial threadline force variations.
3.6.2
Oscillating
Feed Roller Surface Speed
Wear on the feed roller surface can cause an oscillating
rate of material delivery to the texturing zone.
202
As the rate
of material delivery changes, so do threadline forces.
To
help understand how the frequency of oscillation of the
material delivery rate affects threadline forces, we execute
the transient analysis given in Section 3.3 and program the
feed roller velocity to oscillate sinusoidally 1% above and
below the nominal throughput speed of 0.294 inches per
second.
The frequency of forced disturbances are:
0.0393 Radians per Second (.1 x Feed Roller Speed)
0.393
Radians per Second ( 1 x Feed Roller Speed)
3.93
Radians per Second (10 x Feed Roller Speed)
The machine dimensions used in the analysis are the ones
for Mode I described in Section 3.4.
twist is 60 TPI.
The programmed machine
Below we present the peak to peak variation
ratio for Feed Roller Speed and for the corresponding threadline tension and threadline torques
FREQUENCY OF
FORCED DISTURBANCE
PEAK TO PEAK VARIATION RATIO
ROLLER
THREADLINE
SPEED.
TENSION
THREADLINE
TORQUE
.0393 Radians/sec
.02
.101
.077
0.393
Radians/sec
.02
.052
.041
3.93
Radians/sec
.02
.006
.005
For the analytical model using Mode I machine dimensions,
the entire threadline length is 23.25 inches.
Commercial
machines generally have a threadline length an order of magnitude
greater than this length.
203
If the feed roller was
reduced to 1/10 its present radius in our theoretical model
(so that the ratio of roller radius to threadline length were
about that of a commercial machine) its angular velocity
would have to be increased by tenfold to maintain the
original material delivery rate.
Accordingly, the effect
of a worn eccentric feed roller on threadline behavior is
represented by the conditions where the frequency of disturbance is 3.93 radians per second.
Thus, we can conclude
that the effects of small amplitude transients in the
material delivery rate are negligible.
3.6.3
Oscillating Take Up Roller Surface Speed
An analysis identical to the previous analysis in Section
3.6.2 can be undertaken for the case of oscillating take up
roller surface speed.
The results are given below:
FREQUENCY OF
PEAK TO PEAK VARIATION RATIO
FORCED DISTURBANCE
TAKE UP ROLLER THREADLINE
THREADLINE
SPEED
TENSION
TORQUE
0.0629
.02
.052
.024
0.629
.02
.019
.013
6.29
.02
.002
.001
Comparing the results above with the results given in Section
3.6.2 we see that the steadiness of take up rate is not as
critical a parameter as material delivery rate with regard
to variation
of threadline forces.
This can be attributed
to the significantly higher cold fiber tensile modulus than
the hot fiber
"modulus".
204
3.7
EFFECT OF INCREASING YARN WRAP ANGLE ON SPINDLE
In Section 2.3.9 we showed that the linear velocity
of the twisted yarn, V 3, as it enters the spindle is minimally affected by the range of yarn-spindle contact frictional forces which generally obtain in the texturing process.
However if the contact friction is significantly increased,
V3 must accordingly decrease.
This decrease of V 3 will
reduce the texturing zone tensions and the
filaments in the hot zone will be drawn to a lesser degree.
Likewise the threadline torque will be reduced if the texturing
tension decreases.
A simple way to increase the frictional forces acting
against threadline translational movement is to increase the
the yarn wrap angle around the spindle pin.
Experiments were
conducted with the Du Pont POY PET used earlier for the
transient study to examine the effect of double wrapping the
yarn around the spindle pin on threadline behavior.
Figures 3.48, 3.49, 3.50,
and 3.51 show significant
differences in threadline behavior depending on whether
the
yarn is double wrapped or single wrapped around the spindle
pin.
When the yarn is double wrapped both steady state and
transient values of threadline torque and tension are about
15% lower than the corresponding values when the yarn is only
single wrapped.
Note however that the time response is rela-
tively independent with regard to wrap angle.
205
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Chapter
4
PERIODIC TWIST SLIPPAGE
The translation of spindle rotation into texturing threadline rotation is clearly dependent on friction forces.
The
generation of these forces is due to the external contact
between the yarn and spindle surfaces as well as the internal friction deformation of the yarn as it traverses the
spindle
5)
The contact friction forces are dependent on
surface conditions (yarn and spindle), threadline tension,
and relative velocity between the yarn and spindle(16);
the internal forces are generated by rotation of the yarn in
a bent configuration around the pin (15)
Rotation under such
flexural conditions will cause cycling of tensile and compressive stresses within the cross section of the yarn which
leads to interfiber slippage resulting in energy losses in
the yarn due to its viscoelastic behavior and inherent loss
modulus.
Both of these internal forces act in opposition
to the relative motion between the yarn and spindle pin. (1 5 )
Thus, internal and external contact activated friction
torque join together to balance the combined threadline
torque and post spindle torque according to the following
relation:
M
+ M.
1i
Me
=
where M
=
e
threadline
post spindle
(4-1)
(4-1)
external contact friction activated
torque
210
Mi
=
internal friction activated torque
Mthreadline
=
Mpost spindle=
texturing zone torque
post spindle zone torque
More to the point, the potential internal and external
(contact) frictionally activated torque should be equal or
exceed the combined threadline torques of equation (4-1).
Yarn-Pin Contact Friction Induced Torque
The standard capstan equation for yarn friction on a
capstan
where
is:
8
T 22
=
T1 e
T2
=
post capstan tension
T1
=
pre capstan tension
=
coefficient of contact friction between
yarn and pin
wrap angle of yarn around pin perimeter
0
=
Sasaki and Kuroda(
(4-2)
show that for textile yarns this simple
relation is not entirely accurate and that there is an extra
increment of tension resulting from yarn bending.
How-
ever as a first approximation we will assume that the capstan
equation may be used to determine the coefficient of friction
between the yarn and spindle.
Experimental work was carried out to determine the values
of T 1 and T 2 (pre and post spindle tension) for a range of
machine conditions.
The yarn tested was the POY PET used for
steady state and transient experiments described earlier.
The results are listed in Table 4.1.
211
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212
To determine the yarn-pin friction induced torque, the
normal force between the yarn and spindle pin per unit length
must be multiplied by the yarn radius and the coefficient of
yarn-spindle friction and the product integrated around the
full spindle wrap to obtain:
M
e
T
Threadline
R
yarn
( e2
-l
(4-3)
Applying the measured coefficients of friction given in
Table 4.1 to equation (4-3) , we can thus determine yarnpin frictionally induced torque which acts to rotate the
texturing threadline.
Table 4.1 lists these externally
developed torques and the measured threadline torques.
Comparisons of the values of measured threadline torque
and external torque supplied by the spindle shows that the
torque thus developed falls short of the threadline torque
required for steady state operation.
It would appear that the
deficit in the required torque is made up by the internal
torque developed when the yarn also rotates in the bent state
(around its own axis) as it traverses the spindle pin.
From
the diagram 4.1 (where twist T is plotted against wrap angle
)
it can be seen that there is constant slippage (Tmachine-T)
over the entire yarn loop on the spindle surface.
ence (Tmachine-T8)
The differ-
is caused by the untwisting of the yarn as
it proceeds on the pin surface.
Observations of the twist
around the pin indicates that most of the untwisting occurs
in the last quadrant of the spindle surface perimeter. (4)
213
Figure 4.1
TYPICAL TWIST DISTRIBUTIONS ON A PIN-SPINDLE
, E SMALL
E
,E LARGE
E-r
E
W
U
H
toe
PJ
0
2ir
WRAP ANGLE
(
TP= MACHINE TWIST
T = TWIST AT WRAP ANGLE
iH
,E= FRICTION TORQUE (INTERNAL AND EXTERNAL)
1 TWIST ·DISTRIBUTION
2 TWIST DISTRIBUTION
214
This condition is shown as Twist Distribution 1.
case the sum of Me + M
For this
would be relatively large.
If the
sum of Me + Mi is considerably less than that for Twist
Distribution 1 twist can be pictured as Twist Distribution
2 over the spindle surface.
The efficiency of this yarn-
spindle system is now less than 100%, i.e. the yarn in the
cooling zone rotates less than one time for each spindle rotation.
During steady state operation with the slippage
envisioned for Twist Distribution 2
no real twist will
manifest itself in the post spindle region since one pitch
length of twisted yarn enters the spindle for each rotation of
the cooling yarn segment.
This continual rotational slippage
need not affect product quality but obviously affects process
productivity.
Tight Spots
Rotational slippage at the spindle pin may take place on a
steady state basis as has been pointed out.
This need not
promote product irregularity, only loss in process efficiency.
But if rotational slippage takes place periodically or in an
irregular manner, an inequality will occur between the time
period of twist-pitch translation and the rotation time period
of the cooling yarn as it enters the spindle.
When this con-
dition occurs, real twist will appear in the post spindle zone.
Real twist can also appear downstream of the spindle without
rotational slippage,-- but rather in presence of translational
215
spurting or acceleration.
For this condition also develops
an inequality between the period of twist-pitch translation
and the period of cooling yarn rotation.
Such spurting can
cause a tight spot in the existing yarn, i.e. a short yarn
segment of high twist amidst long segments of virtually
untwisted yarn.
The tight(twist) spot prevents local crimp
development and causes the appearance of a "pin hole" in the
fabric.
A picture of a tight spot is shown in Figure 4.2.
This
tight spot was formed as a result of the spindle speed being
suddenly reduced on the MITEX False Twister after the machine
had been operating at steady state.
The operating conditions
were:
Cold Zone Length
6.00 inches
Machine Draw Ratio 1.60
Heater Length
1.25 inches
Heater Temperature 210 0 C
Cooling Zone Length
7.00 inches
Yarn 245/30 POY PET
Post Spindle Length
9.00 inches
Machine Twist 60 TPI+50
In the first instant that the spindle speed is reduced,
the translational movement of the twist pitch continues as
before, and now the rotational period of the pin is greater
than the time for the advance of one twist pitch.
As a result
each turn advanced into the pin is no longer fully untwisted
and some real twist starts to build up in the post spindle
zone.
216
TIGHT SPOT
Cold Length
Heater
6"
1.25"
Cooling
Post Spindle
7"
Machine Draw Ratio
1.60"
Heater Temperature
210
Yarn
245/30
Spindle Speed
60-50
9"'
POY PET
The reduced rotational speed of the pin results in reduced
rotational speed of the cooling zone, and, in turn in a
reduced twisting rate at cold and hot entrances.
With this
step reduction in twisting rate, the threadline tension and
torque in the texturing zone drop precipitously.
This marked
drop in tension upstream of the spindle pin and the slight
increase of tension downstream (which is expected because
of the real twist occuring in that zone) cause a tension
gradient greater than that which can be accommodated by the
translational frictional constraint around the pin.
Trans-
lational spurting will result, carrying segments of high
level real twist into the post spindle zone.
This small section of real twist which is of the same sense
as the threadline twist does not spread out uniformly in the
post spindle zone threadline.
Instead it remains concen-
trated and can easily be observed.
The persistence of this concentration of real twist lies
in the nature of the torsional behavior of the texturing
threadline.
As steady state, the texturing threadline is
entirely untwisted as it leaves the spindle and enters the
post spindle zone at a small negative torque,(see level C in
Figure 4.3). If for any reason, translational spurting takes
place in the threadline moving about the spindle pin or sudden
rotational slippage takes place,a yarn segment with real twist
218
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%-
4
in
z
a
Or
M
4
z
MI
I-
0
z
I-
a.
0
)m
M.
IO
Ig
z
0
Ws
Ik
ill
3E
(D
rI
i
.:
O
(t.O)
-
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_.
eO
notuoL
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I
I
O0
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0
O
0
0
o
-
O
W)
142
o0
.
.
O
.d
o
ok.
t
qr
at torque level A will enter the post spindle zone.
yarn further
Untwisted
downstream in the post spindle zone at torque
level C will then uptwist slightly and the tight spot will
downtwist further until the torque in both segments are
equal at level B where the twist level in the tight spot
is observed to be 50 TPI (about half the threadline twist).
The persistence of the tight spot in the post spindle zone
is thus attributable to the presence of two different
mechancially connected portions of threadline having equal
torque but entirely unequal twist geometry.
When the spindle speed is suddenly increased after the
process is operating at steady state, real twist of opposite
sense to that of the threadline twist appears in the post
spindle threadline, spread out uniformly and no tight spots
are observed.
Observation of transient texturing zone tension during
twist increases reflects marked increase in pre-spindle
tension and slight increase in post spindle tension.
This
condition precludes translational spurting and hence the
appearance of segments of concentrated twist.
220
Continual Occurrence of Tight Spots Along with Threadline
Tension and Torque Oscillation
For steady state operation in draw texturing, the torque
equality of equation (4.1) obtains.
If for some reason the
torque generating capacity of the yarn-pin system suddenly
fails or if the torque requirement of the texturing threadline suddenly increases, then rotational slippage will occur
over the entire contact perimeter of the pin.
As a result the
rotational speed of the cooling zone will drop precipitously
and following this, the threadline tension and torque will
rapidly decline as was seen in Section 3.4.
Translational
surging and the appearance of tight spots may accompany this
drop in texturing tension.
When sudden reduction in rotational velocity of the cooling
threadline occurs as a result of a stepwise reduction in spindle speed the tensile and torque drop observed will recover
after a period of time due to propagation of the new twist
level through the machine (and elimination of the effect of
transient twist contraction).
In the case at hand the tension
and torque decline may be checked for other reasons, e.g.
because of re-establishment of the torque generating capacity
of the yarn-pin system so as to satisfy equation (4.1).
The component of torque generation at the pin which is due
to yarn-pin frictional contact can be shown to depend approximately on the level of threadline tension according to
221
Figure 4.4
PREDICTED THREADLINE TORQUE AND TENSION CYCLING
MACHINE LENGTH 23.25 "
to
THROUGHPUT SPEED .4704 "/sec
2t.0
E
0 22.0
-I
I
\
0
c0 20.0
,o
18.0
I6.0
I
2.0
1.8
o
p
I
I
I
1.6
s
0..
I-
1.2
I
0.0
I
20.0
I
40.0
I
I
80.0
I
100.0
Time, secovcds
222
I
120.0
equation (4.3). Likewise one can show that the internally
generated torque in a yarn which is rotated in a bent configuration (around the pin) will depend on the level of threadline tension.
Thus the sum of components of torque generation
at the pin can be related to texturing tension.
For rotational slippage to persist, the total torque generated at the pin must be less than the torque required for
non-slip texturing.
Or conversely, if the texturing line
torque falls below the yarn-pin generated torque, slippage
will cease.
Figure 4.4 shows the reduction in line tension and torque
which occurs in dotted lines as a result of an initial (unspecified) rotational slippage.
The tension value of Figure
4.4 calculated from our transient analysis is used to calculate a generated torque by multiplying by a constant (corresponding to the steady ratio of torque to tension).
The indi-
cated torque value in Figure 4.4 is also calculated from our
transient analysis.
The system is forced to bottom out when
the above calculated transient torque falls below the generated torque.
At this instant the slippage ceases and the ro-
tational speed of the cooling zone assumes the speed of the
spindle. This is now equivalent to a step increase in cooling
zone rotational speed and yarn tension and torque will rise
accordingly as calculated from the transient analysis and
plotted in solid lines in Figure 4.4.
223
The increasing tension value, will according to the transient analysis, overshoot its steady state value, even while
the torque is still rising.
Here again we find a situation
when the total yarn pin generated torque falls below the instant threadline torque and the onset of rotational slippage
at the pin occurs, -- again being designated in Figure 4.4 by
the dotted lines.
This type of cycling will persist so long
as the material and machine parameters are set so as to enhance system sensitivity to cycling.
Experience has shown
that system sensitivity to cycling is suppressed by proper
choice of yarn lubricant and by increasing the ratio of post
spindle tension to pre-spindle tension.
Finally it should be pointedout that the internally generated torque in a bent, rotating yarn, will depend on twist
level as well as on tension, the lower the twist the greater
the internal fiber slippage hence the greater the torque generated.
This dependence suggests that twist changes occuring
at the heater entrance because of changing threadline rotational speeds will affect internal frictional torque generation
once the twist change reaches the spindle pin.
224
Chapter
5
CONCLUSIONS AND SUMMARY
Steady State Operation of the Draw Texturing Process
During steady state operation of the draw texturing process
there are essentially two levels of twist in the threadline
between the feed rollers and spindle.
In one segment of the
threadline (over the heater and beyond) the twist level is
determined simply by the spindle speed and the yarn throughput
speed.
Upstream of this segment lies the threadline cold zone
where the twist level is somewhat less.
In absence of fric-
tional contact between yarn and heater threadline tension and
torque will be constant from position to position between the
feedrolls and the spindle. The introduction of twist takes
place in essence, at two zones in the system: at the entrance
to the cold zone and at the entrance to the hot zone.
The
equality of tension and torque at these zones suggests that
their local twist levels will be inversely proportional to
their effective torsional rigidities and this is what we predict analytically and observe experimentally.
The torsional
resistance at the entry to the coldzone is seen to depend on fiber
bending and torsional rigidity as well as on filament tension;
at the heater entry,the bending and torsional stresses are
thermally relaxed with only the tensile component of yarn torsional rigidity remaining.
Thus the twist level in the hot
225
zone far exceeds
that of the cold zone.
The threadline
tension is developed as an aggregate of the filament tensile
components along the yarn axis.
The threadline torque is
developed as an aggregate of the components of filament bending moments and twisting moments, to the degree that they
exist,
and of the moments due to filament tension.
The pre-
diction of threadline tension and torque therefore requires
the determination of the filament-system constitutive relations, the local yarn geometry, and the system compatibility
at the entrance to the cold and hot zones.
Our analysis pre-
dicts that as the operating level of machine twist is increased, with machine draw ratio and heater temperature kept constant, threadline tension decreases, while threadline torque
increases.
This seemingly contrary behavior can be attributed
to the increase in local filament helix angles in outer layers
of the yarn, which reduces the yarn axial component of filaAs
ment tension and increases the circumferential component.
the twist increases, the variation of draw ratios in different
filament layers in the yarn drawing neck also increases.
It
is predicted that the temperature of the heater (over the
range of interest) should not affect threadline behavior significantly.
This follows from the fact that over the range
of common texturing conditions, temperatures have minimal
effect on (hot) drawing forces.
Lastly it is predicted that if the cold filament bending
226
rigidity or torsional rigidity is increased, both threadline
torque and tension will increase while cold zone twist level
will decrease.
Hot zone twist should remain unchanged since
this twist level is indicated to be a function solely of yarn
throughput speed and spindle speed.
Numerous experiments were conducted on DuPont POY polyester
yarns for the purpose of comparing measured values of threadline parameters, i.e. threadline tension, torque and twist
levels with predicted results during steady state operation of
the draw texturing process.
The agreement between predicted
and measured values is within 9.3% for tension, 12.2% for
torque, 12.3% for hot twist and 10.9% for cold twist.
227
Transient Operation of the Draw Texturing Process
It has been observed during texturing that when spindle
speeds are suddenly altered, the first signs of twist change
in the threadline occur at the cold zone entrance and at the
heater.
These observations provided the basis for the hy-
pothesis that torsional rigidity of the texturing threadline
is significantly lower at the cold zone entrance and heater
than for the rest of the threadline existing between the feed
rollers and spindle.
Torsional disturbances in the threadline
are evidenced primarily as twist changes at the 'soft' zones
and these changes then propagate downstream with yarn movement.
Thus, the formation rigidities of the texturing threadline
essentially reflect the rigidity of the soft forming zones
under the conditions of local twist insertion.
On the other
hand, the transient twist response of cold zone and cooling
zone segments to incremental changes in spindle speed reflects
the very high incremental torsional rigidity of these threadline segments.
To test these hypotheses we have measured the torsional
rigidity of cold and cooling zone yarn segments and these were
seen to be several orders of magnitude greater than the cold
forming 'rigidity' and the hot uptwisting 'rigidity'. One can
attribute these rigidity differences to the
ariation in
twisting deformation modes at each of the soft zones and in
segments which lie downstream of these zones.
228
Observations of dynamic twist formation in larger models
indicate that many filaments approaching the twist triangle
apex are already twisted around their axes and sometimes
around neighboring pairs.(13)
They are then wound onto the
newly formed end of the yarn, with little additional twisting
observed thereafter.
After the twist is inserted at the cold
zone entrance, interfilament friction and transverse stresses
cause the yarn to behave like a helically anisotropic solid
rod with subsequent high torsional rigidity.
The situation at the uptwist zone at the heater involves
sudden stress relaxation or softening of the filaments.
The
requirement of constant threadline torque in the presence of
this stress relaxation results in a cranking up of twist at
the heater.
As the new hot twist level is reached lateral
forces due to filament tensions and local curvatures will
also reach a new high level.
This increased interfilament
pressure accompanied by thermal softening will result in
lateral compressive creep and in growth in contact areas between filaments.( 9)
Higher friction and interfilament shear
stresses will then result in higher incremental torsional
rigidities.
In our analysis of transient operation of the draw texturing process we have considered the response of the threadline
to-torsional disturbances, i.e. to changes in spindle speed.
We reason that transient operation generates material build-
229
ups and twist buildups with respect to time in different zones
of the texturing system and 'bookkeeping' of these buildups
must be based on how the buildups distribute within each zone
of the threadline.
Further, the material and turn balances
for each zone are coupled with the requirement of threadline
tension and threadline torque uniformity throughout the texturing zone.
The transient analysis predicts that if the spindle speed
is increased stepwise the threadline torque responds by rising
sharply with time and then slowly settling to a new value
higher than the steady state value before the spindle speed
was increased while the threadline tension increases sharply
and then settles to a value which was less than the previous
value.
Correspondingly, if the spindle speed is decreased
stepwise the threadline tension and torque should decrease
precipitously before the threadline tension settles to a new
value, higher than the previous value while the torque settles
to a new value, lower than the previous value.
Under certain
conditions, this type of transient threadline response increases the prospect of threadline tension and torque cycling.
For example if rotational slippage of the yarn on the spindle
occurs the system reacts as if there were a step change in
spindle speed, and recurrence of such slippage will lead to
tension, torque and twist cycling in a texturing process nominally operating at steady state.
230
Numerous experiments were conducted using Du Pont POY
polyester yarns for the purpose of comparing measured values
of threadline paramenters, i.e. threadline tension, torque,
and twist levels with predicted results during transient
operation of the draw texturing process.
We used Analytical
Model 2(tilted twist distribution) and the agreement with
respect to time response and absolute levels of threadline
parameters was good.
Additional experiments were conducted
using Du Pont POY nylon yarns to reinforce our confidence
in the utility of the analysis of texturing threadline
behavior.
There was a persistent 10%
difference in the
predicted and measured values of threadline tension and
threadline torque.
However the predicted and measured time
response of the system was indeed favorable.
231
Chapter
6
SUGGESTIONS FOR CONTINUING RESEARCH
A number of suggestions for continuing research are
presented below.
The experimental results and mathematical
analyses here presented should provide the direction for
continuing research in this rapidly developing segment of
industrial technology.
1.
Characterization of the Torsional Rigidity of
Threadline Segments Over the Heater : The torsional
rigidity of yarn segments taken from the cold zone and
cooling zone has been determined.
Likewise, we have deter-
mined the "formation rigidity" of yarn segments at the cold
zone entrance and the hot zone entrance.
Further, we reasoned
that the yarn over the entire heater acts as a soft zone since
observation of transient twist over the heater did not indicate any change in its distribution with time.
With the use
of very short heaters in our experimental machine, the spreading of the "soft zone" over the heater does not disturb the
physics of the situation unduly.
But further understanding
of this important distribution is necessary because of the
significantly longer heater lengths which are used in
commercial machines and because of the difference in heat
transfer characteristics.
232
2.
Effect of Sinusoidally Imposed Machine Disturbances
on Threadline Response:
Our experiments conducted to study
transient operation of draw texturing processes utilized
step changes in spindle speeds to disturb the texturing
system.
More realistic to commercial application would be
a sinusoidal machine disturbance such as could be implemented
by use of programmable drive motors designed to deliver shaft
speeds which vary with time.
Results from such experiments
could then be compared with the transient results predicted
in our analysis.
3.
Tension Ratio Over the Spindle During Transient
Operation:
As a basis for understanding the nature of twist
slippage past the spindle it is important that threadline
tensions before and after the spindle be measured simultaneously with spurting of the threadline.
The pattern of
changing tension gradients could then be compared with the
lengthwise distribution of tight spots along the threadline.
4.
Twist Geometry Around the Spindle Pin:
It has been
proposed that whenever there is a sudden increase in the
in the tension gradient around the spindle pin, a threadline
translational surge takes place, accompanied by a tensile
jerk upstream of the spindle.
This tension increase acting
on the yarn in the hot zone causes a proportional increase
in line torque.
The latter is accompanied by a twist increase
233
at the cold formation zone in order to keep threadline torque
uniform in the texturing zone.
can cause local buckling
Such a sudden twist increase
which may persist in the threadline.
Upon traversing the spindle pin surface such a local buckle
might cause another translation surge which would result in
still another buckling, etc.
Photographic study is necessary
to confirm this behavior.
234
BIBLIOGRAPHY
1.
Mey, W., Annual Conference of the Textile Institute,
Baden-Baden, 1966.
2.
Thwaites, J.J., Linear Density Variations in Draw
Textured Yarns, J. Textile Institute, 65, 1974, P. 353.
3.
Quynn, R.G., Pre-Oriented Polyester as a Feed Yarn for
Simultaneous Draw Texturing, Textile Research Journal,
45, 1975, P.88.
4.
Backer, S. and Yang, W.L., Mechanics of Texturing
Thermoplastic Yarns, Part I: Experimental Observations
of Steady State Texturing, Textile Research Journal,
(in press).
5.
Platt, M.M., Klein, W.G., Hamburger, W.J., Torque
Development in Yarn Systems: Singles Yarn, Textile
Research
6.
Journal,
28, 1958, P.1.
Naar, R.Z., Steady State Mechanics of the False Twist
Yarn Texturing Process, Sc. D. Thesis, Department of
Mechanical Engineering, M.I.T., Cambridge, Massachusetts,
1975.
7.
Morton, W.E., The Arrangement of Fibers in Singles Yarns,
Textile Research Journal, 26, P. 235.
8.
Hearle, J.W.S., Form and Fiber Arrangement in Twisted
Yarns, Chapter 3 in Hearle, J.W.S., Grosberg, P., and
Backer, S., Structural Mechanics of Fibers, Yarns, and
Fabrics, Volume I, Wiley-Interscience, New York, 1969.
235
9.. Brookstein, D.S.,. On the Mechanics of Draw Texturing,
M.S.
Thesis, Department of Mechanical Engineering,
M.I.T., Cambridge, Massachusetts, 1973.
10.
Shealy, O.L., and Kitson, R.E., An Age-Stable Feed
Yarn for Draw Texturing, Textile Research Journal, 45,
1975, P. 112.
11.
Ward, I.M., Mechanical Properties of Solid Polymers,
Wiley-Interscience, New York, 1971, P. 245.
12.
Backer, S., and Yang, W.L., Mechanics of Texturing
Thermoplastic Yarns, Part II:
Experimental Observations
of Transient Behavior, Textile Research Journal, (in press)
13.
El-Shiekh, A, H., On the Mechanics of Twist Insertion,
Sc. D. Thesis, Department of Mechanical Engineering,
M.I.T., Cambridge, Massachusetts, 1965.
14.
Thwaites, J.J., Mechanics of Texturing Thermoplastic
Yarns, Part IV:
The Origin and Significance of the
Torsional Behavior of the False Twist Threadline, Textile
Research Journal, (in press).
15.
Ostertag, C., Trummer, A., Theoretical Analysis of the
Influence of Internal Yarn Friction on the Twist in
False Twisting,
Symposium on Man Made Fiber Technology,
Part II, 70 th National Meeting, American Institute of
Chemical Engineers, 1971.
236
16.
Olsen, J.S., Frictional Behavior of Textile Yarns,
Textile Research Journal, 39, 1969, P. 31.
17.
Sasaki, T., and Kuroda, K., Additional Tension Caused
by Bending of a Yarn on a Slender Cylinder, J. Textile
Machinery Society of Japan, 20, No.2 (English Edition)
1974, P.30.
237
APPENDIX
1
INERTIA EFFECTS ON THREADLINE
TRANSLATIONAL MOMENTUM FORCE
DV
where D = Yarn Denier
V = Translational Velocity
of Yarn
For the yarns processed (70 to 250 denier) at speeds
up to 1 inch per second the translational momentum
force is 1.23 x108
GPD compared to .1 GPD tensions.
ROTATIONAL MOMENTUM FORCE
I
where I= Polar Moment of Inertia
2
w= Angular Velocity of Yarn
For the yarns processed (70 to 250 denier) at angular
speeds up to 250 radians per second the angular
momentum
torque is 1.12 x 10-9 in lbs compared
typical threadline
torques of 1.0 x 10
238
-4
to
in lbs.
APPENDIX 2
EXPERIMENTAL
VALUES
OF THREADLINE
TENSION
AND TORQUE
(each data point represents the average
of at least 20 points)
239
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APPENDIX
4
MITEX TORQUE- TENSION
METER
Threadline torque and threadline tension are measured online during texturing by the MITEX Torque-Tension Meter(IDR
Needham, MA.).
The meter sensitivity is on the order of 1
millivolt output per gram of threadline tension and 1 millivolt
per 1 x 10- 6 in lbs of threadline torque.
The principles of operation are as follows.
Untwisted
feeder yarn which is to be textured enters the device and is
wrapped ninety degrees around a near frictionless pulley.
The
yarn line of action upstream of action is directed through the
center of a flexural pivot (pivot A).
This pivot twists
a calibrated amount when threadline tension imposes a net
torque on it.
After the yarn travels past the pulley it
proceeds through the threadline torque pivot and is then
wrapped around a smooth shaft (3600) which traps twist from the
texturing threadline and prevents it from bleeding pat the defined cold zone entrance.
Threadline torque twists the torque
pivot(pivot B) a calibrated amount proportional to the threadline torque.
The displacement angle of the torque pivot and the tension
pivot is detected by metal flags connected to these pivots
which are part of variable push-pull capacitor systems.
244
MITEX TORQUE TENSION METER
YARN
245
Laboratory False Twist Machine
-u··---YI--r-rr·-*-·u--L-·l-
1-··-·-
--^-I
·- -iU-·
-r ^···--r---
-^--·---·---
L--·--
·- 1I1 -
Torque -Tension
Meter
APPENDIX
5
COMPUTER PROGRAM FOR STEADY STATE ANALYSIS
247
MlTLibraries
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